diff --git a/openmc/aggregate.py b/openmc/aggregate.py
new file mode 100644
index 0000000000..c77b94ad76
--- /dev/null
+++ b/openmc/aggregate.py
@@ -0,0 +1,404 @@
+import sys
+from numbers import Integral
+
+import numpy as np
+
+from openmc import Filter, Nuclide
+from openmc.cross import CrossScore, CrossNuclide, CrossFilter
+from openmc.filter import _FILTER_TYPES
+import openmc.checkvalue as cv
+
+
+if sys.version_info[0] >= 3:
+    basestring = str
+
+# Acceptable tally aggregation operations
+_TALLY_AGGREGATE_OPS = ['sum', 'mean']
+
+
+class AggregateScore(object):
+    """A special-purpose tally score used to encapsulate an aggregate of a
+    subset or all of tally's scores for tally aggregation.
+
+    Parameters
+    ----------
+    scores : Iterable of str or CrossScore
+        The scores included in the aggregation
+    aggregate_op : str
+        The tally aggregation operator (e.g., 'sum', 'mean', etc.) used
+        to aggregate across a tally's scores with this AggregateScore
+
+    Attributes
+    ----------
+    scores : Iterable of str or CrossScore
+        The scores included in the aggregation
+    aggregate_op : str
+        The tally aggregation operator (e.g., 'sum', 'mean', etc.) used
+        to aggregate across a tally's scores with this AggregateScore
+
+    """
+
+    def __init__(self, scores=None, aggregate_op=None):
+
+        self._scores = None
+        self._aggregate_op = None
+
+        if scores is not None:
+            self.scores = scores
+        if aggregate_op is not None:
+            self.aggregate_op = aggregate_op
+
+    def __hash__(self):
+        return hash(repr(self))
+
+    def __eq__(self, other):
+        return str(other) == str(self)
+
+    def __ne__(self, other):
+        return not self == other
+
+    def __deepcopy__(self, memo):
+        existing = memo.get(id(self))
+
+        # If this is the first time we have tried to copy this object, create a copy
+        if existing is None:
+            clone = type(self).__new__(type(self))
+            clone._scores = self.scores
+            clone._aggregate_op = self.aggregate_op
+
+            memo[id(self)] = clone
+
+            return clone
+
+        # If this object has been copied before, return the first copy made
+        else:
+            return existing
+
+    def __repr__(self):
+        string = ''.join(map(str, self.scores))
+        string = '{0}({1})'.format(self.aggregate_op, string)
+        return string
+
+    @property
+    def scores(self):
+        return self._scores
+
+    @property
+    def aggregate_op(self):
+        return self._aggregate_op
+
+    @scores.setter
+    def scores(self, scores):
+        cv.check_iterable_type('scores', scores, basestring)
+        self._scores = scores
+
+    @aggregate_op.setter
+    def aggregate_op(self, aggregate_op):
+        cv.check_type('aggregate_op', aggregate_op, (basestring, CrossScore))
+        cv.check_value('aggregate_op', aggregate_op, _TALLY_AGGREGATE_OPS)
+        self._aggregate_op = aggregate_op
+
+
+class AggregateNuclide(object):
+    """A special-purpose tally nuclide used to encapsulate an aggregate of a
+    subset or all of tally's nuclides for tally aggregation.
+
+    Parameters
+    ----------
+    nuclides : Iterable of Nuclide or CrossNuclide
+        The nuclides included in the aggregation
+    aggregate_op : str
+        The tally aggregation operator (e.g., 'sum', 'mean', etc.) used
+        to aggregate across a tally's nuclides with this AggregateNuclide
+
+    Attributes
+    ----------
+    nuclides : Iterable of Nuclide or CrossNuclide
+        The nuclides included in the aggregation
+    aggregate_op : str
+        The tally aggregation operator (e.g., 'sum', 'mean', etc.) used
+        to aggregate across a tally's nuclides with this AggregateNuclide
+
+    """
+
+    def __init__(self, nuclides=None, aggregate_op=None):
+
+        self._nuclides = None
+        self._aggregate_op = None
+
+        if nuclides is not None:
+            self.nuclides = nuclides
+        if aggregate_op is not None:
+            self.aggregate_op = aggregate_op
+
+    def __hash__(self):
+        return hash(repr(self))
+
+    def __eq__(self, other):
+        return str(other) == str(self)
+
+    def __ne__(self, other):
+        return not self == other
+
+    def __deepcopy__(self, memo):
+        existing = memo.get(id(self))
+
+        # If this is the first time we have tried to copy this object, create a copy
+        if existing is None:
+            clone = type(self).__new__(type(self))
+            clone._nuclides = self.nuclides
+            clone._aggregate_op = self._aggregate_op
+
+            memo[id(self)] = clone
+
+            return clone
+
+        # If this object has been copied before, return the first copy made
+        else:
+            return existing
+
+    def __repr__(self):
+
+        string = '{0}('.format(self.aggregate_op)
+
+        # Append each nuclide in the aggregate to the string
+        for nuclide in self.nuclides:
+            if isinstance(nuclide, Nuclide):
+                string += '{0}, '.format(nuclide.name)
+            else:
+                string += '{0}, '.format(str(nuclide))
+
+        string += ')'
+        return string
+
+    @property
+    def nuclides(self):
+        return self._nuclides
+
+    @property
+    def aggregate_op(self):
+        return self._aggregate_op
+
+    @nuclides.setter
+    def nuclides(self, nuclides):
+        cv.check_iterable_type('nuclides', nuclides, (Nuclide, CrossNuclide))
+        self._nuclides = nuclides
+
+    @aggregate_op.setter
+    def aggregate_op(self, aggregate_op):
+        cv.check_type('aggregate_op', aggregate_op, basestring)
+        cv.check_value('aggregate_op', aggregate_op, _TALLY_AGGREGATE_OPS)
+        self._aggregate_op = aggregate_op
+
+
+class AggregateFilter(object):
+    """A special-purpose tally filter used to encapsulate an aggregate of a
+    subset or all of a tally filter's bins for tally aggregation.
+
+    Parameters
+    ----------
+    filter : Filter or CrossFilter
+        The filter included in the aggregation
+    filter_bins : Iterable of tuple
+        The filter bins included in the aggregation
+    aggregate_op : str
+        The tally aggregation operator (e.g., 'sum', 'mean', etc.) used
+        to aggregate across a tally filter's bins with this AggregateFilter
+
+    Attributes
+    ----------
+    filter : filter
+        The filter included in the aggregation
+    filter_bins : Iterable of tuple
+        The filter bins included in the aggregation
+    aggregate_op : str
+        The tally aggregation operator (e.g., 'sum', 'mean', etc.) used
+        to aggregate across a tally filter's bins with this AggregateFilter
+
+    """
+
+    def __init__(self, filter=None, bins=None, aggregate_op=None):
+
+        self._type = '{0}({1})'.format(aggregate_op, filter.type)
+        self._bins = None
+        self._stride = None
+
+        self._filter = None
+        self._aggregate_op = None
+
+        if filter is not None:
+            self.filter = filter
+        if bins is not None:
+            self.bins = bins
+        if aggregate_op is not None:
+            self.aggregate_op = aggregate_op
+
+    def __hash__(self):
+        return hash((self.type, self.bins, self.aggregate_op))
+
+    def __eq__(self, other):
+        return str(other) == str(self)
+
+    def __ne__(self, other):
+        return not self == other
+
+    def __repr__(self):
+        string = 'AggregateFilter\n'
+        string += '{0: <16}{1}{2}\n'.format('\tType', '=\t', self.type)
+        string += '{0: <16}{1}{2}\n'.format('\tBins', '=\t', self.bins)
+        return string
+
+    def __deepcopy__(self, memo):
+        existing = memo.get(id(self))
+
+        # If this is the first time we have tried to copy this object, create a copy
+        if existing is None:
+            clone = type(self).__new__(type(self))
+            clone._type = self.type
+            clone._filter = self.filter
+            clone._aggregate_op = self.aggregate_op
+            clone._bins = self._bins
+            clone._stride = self.stride
+
+            memo[id(self)] = clone
+
+            return clone
+
+        # If this object has been copied before, return the first copy made
+        else:
+            return existing
+
+    @property
+    def filter(self):
+        return self._filter
+
+    @property
+    def aggregate_op(self):
+        return self._aggregate_op
+
+    @property
+    def type(self):
+        return self._type
+
+    @property
+    def bins(self):
+        return self._bins
+
+    @property
+    def num_bins(self):
+        if self.filter:
+            return 1
+        else:
+            return 0
+
+    @property
+    def stride(self):
+        return self._stride
+
+    @type.setter
+    def type(self, filter_type):
+        if filter_type not in _FILTER_TYPES.values():
+            msg = 'Unable to set AggregateFilter type to "{0}" since it ' \
+                  'is not one of the supported types'.format(filter_type)
+            raise ValueError(msg)
+
+        self._type = filter_type
+
+    @filter.setter
+    def filter(self, filter):
+        cv.check_type('filter', filter, (Filter, CrossFilter))
+        self._filter = filter
+
+    @bins.setter
+    def bins(self, bins):
+        cv.check_iterable_type('bins', bins, (Integral, tuple))
+        self._bins = bins
+
+    @aggregate_op.setter
+    def aggregate_op(self, aggregate_op):
+        cv.check_type('aggregate_op', aggregate_op, basestring)
+        cv.check_value('aggregate_op', aggregate_op, _TALLY_AGGREGATE_OPS)
+        self._aggregate_op = aggregate_op
+
+    @stride.setter
+    def stride(self, stride):
+        self._stride = stride
+
+    def get_bin_index(self, filter_bin):
+        """Returns the index in the AggregateFilter for some bin.
+
+        Parameters
+        ----------
+        filter_bin : Integral or tuple of Integral or tuple of Real
+            A tuple of value(s) corresponding to the bin of interest in
+            the aggregated filter. The bin is the integer ID for 'material',
+            'surface', 'cell', 'cellborn', and 'universe' Filters. The bin
+            is the integer cell instance ID for 'distribcell' Filters. The
+            bin is a 2-tuple of floats for 'energy' and 'energyout' filters
+            corresponding to the energy boundaries of the bin of interest.
+            The bin is a (x,y,z) 3-tuple for 'mesh' filters corresponding to
+            the mesh cell of interest.
+
+        Returns
+        -------
+        filter_index : Integral
+             The index in the Tally data array for this filter bin. For an
+             AggregateTally the filter bin index is always unity.
+
+        Raises
+        ------
+        ValueError
+            When the filter_bin is not part of the aggregated filter's bins
+
+        """
+
+        if filter_bin not in self.bins:
+            msg = 'Unable to get the bin index for AggregateFilter since ' \
+                  '"{0}" is not one of the bins'.format(filter_bin)
+            raise ValueError(msg)
+        else:
+            return 0
+
+    def get_pandas_dataframe(self, datasize):
+        """Builds a Pandas DataFrame for the AggregateFilter's bins.
+
+        This method constructs a Pandas DataFrame object for the AggregateFilter
+        with columns annotated by filter bin information. This is a helper
+        method for the Tally.get_pandas_dataframe(...) method.
+
+        Parameters
+        ----------
+        datasize : Integral
+            The total number of bins in the tally corresponding to this filter
+
+        Returns
+        -------
+        pandas.DataFrame
+            A Pandas DataFrame with columns of strings that characterize the
+            aggregatefilter's bins. Each entry in the DataFrame will include
+            one or more aggregation operations used to construct the
+            aggregatefilter's bins. The number of rows in the DataFrame is the
+            same as the total number of bins in the corresponding tally, with
+            the filter bins appropriately tiled to map to the corresponding
+            tally bins.
+
+        See also
+        --------
+        Tally.get_pandas_dataframe(), Filter.get_pandas_dataframe(),
+        CrossFilter.get_pandas_dataframe()
+
+        """
+
+        import pandas as pd
+
+        # Construct a sring representing the filter aggregation
+        aggregate_bin = '{0}('.format(self.aggregate_op)
+        aggregate_bin += ', '.join(self.bins) + ')'
+
+        # Construct NumPy array of bin repeated for each element in dataframe
+        aggregate_bin_array = np.array([aggregate_bin])
+        aggregate_bin_array = np.repeat(aggregate_bin_array, datasize)
+
+        # Construct Pandas DataFrame for the AggregateFilter
+        df = pd.DataFrame({self.type : aggregate_bin_array})
+        return df
\ No newline at end of file
diff --git a/openmc/cross.py b/openmc/cross.py
index c03ee51885..9df768b944 100644
--- a/openmc/cross.py
+++ b/openmc/cross.py
@@ -34,7 +34,7 @@ class CrossScore(object):
         The right score in the outer product
     binary_op : str
         The tally arithmetic binary operator (e.g., '+', '-', etc.) used to
-        combine two tally's scores with this CrossNuclide
+        combine two tally's scores with this CrossScore
 
     """
 
@@ -310,7 +310,6 @@ class CrossFilter(object):
             clone._binary_op = self.binary_op
             clone._type = self.type
             clone._bins = self._bins
-            clone._num_bins = self.num_bins
             clone._stride = self.stride
 
             memo[id(self)] = clone
@@ -355,8 +354,8 @@ class CrossFilter(object):
     @type.setter
     def type(self, filter_type):
         if filter_type not in _FILTER_TYPES.values():
-            msg = 'Unable to set Filter type to "{0}" since it is not one ' \
-                  'of the supported types'.format(filter_type)
+            msg = 'Unable to set CrossFilter type to "{0}" since it ' \
+                  'is not one of the supported types'.format(filter_type)
             raise ValueError(msg)
 
         self._type = filter_type
diff --git a/openmc/tallies.py b/openmc/tallies.py
index b66c710965..097d7de3d9 100644
--- a/openmc/tallies.py
+++ b/openmc/tallies.py
@@ -13,6 +13,7 @@ import numpy as np
 
 from openmc import Mesh, Filter, Trigger, Nuclide
 from openmc.cross import CrossScore, CrossNuclide, CrossFilter
+from openmc.aggregate import AggregateScore, AggregateNuclide, AggregateFilter
 from openmc.filter import _FILTER_TYPES
 import openmc.checkvalue as cv
 from openmc.clean_xml import *
@@ -259,6 +260,10 @@ class Tally(object):
     def num_scores(self):
         return len(self._scores)
 
+    @property
+    def num_filters(self):
+        return len(self.filters)
+
     @property
     def num_filter_bins(self):
         num_bins = 1
@@ -460,16 +465,28 @@ class Tally(object):
 
         Parameters
         ----------
-        filter : openmc.filter.Filter
-            Filter to add
+        filter : Filter, CrossFilter or AggregateFilter
+            A filter to specify a discretization of the tally across some
+            dimension (e.g., 'energy', 'cell'). The filter should be a Filter
+            object when a user is adding filters to a Tally for input file
+            generation or when the Tally is created from a StatePoint. The
+            filter may be a CrossFilter or AggregateFilter for derived tallies
+            created by tally arithmetic.
 
         """
 
-        if not isinstance(filter, (Filter, CrossFilter)):
+        if not isinstance(filter, (Filter, CrossFilter, AggregateFilter)):
             msg = 'Unable to add Filter "{0}" to Tally ID="{1}" since it is ' \
                   'not a Filter object'.format(filter, self.id)
             raise ValueError(msg)
 
+        # If the filter is already in the Tally, raise an error
+        if filter in self.filters:
+            msg = 'Unable to add a duplicate filter "{0}" to Tally ID="{1}" ' \
+                  'since duplicate filters are not supported in the OpenMC ' \
+                  'Python API'.format(filter, self.id)
+            raise ValueError(msg)
+
         self._filters.append(filter)
 
     def add_nuclide(self, nuclide):
@@ -477,11 +494,29 @@ class Tally(object):
 
         Parameters
         ----------
-        nuclide : openmc.nuclide.Nuclide
-            Nuclide to add
+        nuclide : str, Nuclide, CrossNuclide or AggregateNuclide
+            Nuclide to add to the tally. The nuclide should be a Nuclide object
+            when a user is adding nuclides to a Tally for input file generation.
+            The nuclide is a str when a Tally is created from a StatePoint file
+            (e.g., 'H-1', 'U-235') unless a Summary has been linked with the
+            StatePoint. The nuclide may be a CrossNuclide or AggregateNuclide
+            for derived tallies created by tally arithmetic.
 
         """
 
+        if not isinstance(nuclide, (basestring, Nuclide,
+                                    CrossNuclide, AggregateNuclide)):
+            msg = 'Unable to add nuclide "{0}" to Tally ID="{1}" since it is ' \
+                  'not a Nuclide object'.format(nuclide)
+            raise ValueError(msg)
+
+        # If the nuclide is already in the Tally, raise an error
+        if nuclide in self.nuclides:
+            msg = 'Unable to add a duplicate nuclide "{0}" to Tally ID="{1}" ' \
+                  'since duplicate nuclides are not supported in the OpenMC ' \
+                  'Python API'.format(nuclide, self.id)
+            raise ValueError(msg)
+
         self._nuclides.append(nuclide)
 
     def add_score(self, score):
@@ -489,19 +524,23 @@ class Tally(object):
 
         Parameters
         ----------
-        score : str
-            Score to be accumulated, e.g. 'flux'
+        score : str, CrossScore or AggregateScore
+            A score to be accumulated (e.g., 'flux', 'nu-fission'). The score
+            should be a str when a user is adding scores to a Tally for input
+            file generation or when the Tally is created from a StatePoint. The
+            score may be a CrossScore or AggregateScore for derived tallies
+            created by tally arithmetic.
 
         """
 
-        if not isinstance(score, (basestring, CrossScore)):
+        if not isinstance(score, (basestring, CrossScore, AggregateScore)):
             msg = 'Unable to add score "{0}" to Tally ID="{1}" since it is ' \
                   'not a string'.format(score, self.id)
             raise ValueError(msg)
 
         # If the score is already in the Tally, raise an error
         if score in self.scores:
-            msg = 'Unable to add a duplicate score {0} to Tally ID="{1}" ' \
+            msg = 'Unable to add a duplicate score "{0}" to Tally ID="{1}" ' \
                   'since duplicate scores are not supported in the OpenMC ' \
                   'Python API'.format(score, self.id)
             raise ValueError(msg)
@@ -509,7 +548,7 @@ class Tally(object):
         # Normal score strings
         if isinstance(score, basestring):
             self._scores.append(score.strip())
-        # CrossScores
+        # CrossScores and AggrgateScore
         else:
             self._scores.append(score)
 
@@ -1599,8 +1638,12 @@ class Tally(object):
             raise ValueError(msg)
 
         new_tally = Tally()
-        new_tally.with_batch_statistics = True
         new_tally._derived = True
+        new_tally.with_batch_statistics = True
+        new_tally._num_realizations = self.num_realizations
+        new_tally._estimator = self.estimator
+        new_tally._with_summary = self.with_summary
+        new_tally._sp_filename = self._sp_filename
 
         # Construct a combined derived name from the two tally operands
         if self.name != '' and other.name != '':
@@ -1698,14 +1741,21 @@ class Tally(object):
                 new_score = CrossScore(self_score, other_score, binary_op)
                 new_tally.add_score(new_score)
 
-        # Correct each Filter's stride
-        stride = new_tally.num_nuclides * new_tally.num_scores
-        for filter in reversed(new_tally.filters):
-            filter.stride = stride
-            stride *= filter.num_bins
+        # Update the new tally's filter strides
+        new_tally._update_filter_strides()
 
         return new_tally
 
+    def _update_filter_strides(self):
+        """Update each filter's stride based on the tally's nuclides and scores
+        for derived tallies created by tally arithmetic.
+        """
+
+        stride = self.num_nuclides * self.num_scores
+        for filter in reversed(self.filters):
+            filter.stride = stride
+            stride *= filter.num_bins
+
     def _align_tally_data(self, other, filter_product, nuclide_product,
                           score_product):
         """Aligns data from two tallies for tally arithmetic.
@@ -1855,17 +1905,9 @@ class Tally(object):
                 if other_index != i:
                     other._swap_scores(score, other.scores[i])
 
-        # Correct the stride for other filters
-        stride = other.num_nuclides * other.num_scores
-        for filter in reversed(other.filters):
-            filter.stride = stride
-            stride *= filter.num_bins
-
-        # Correct the stride for self filters
-        stride = self.num_nuclides * self.num_scores
-        for filter in reversed(self.filters):
-            filter.stride = stride
-            stride *= filter.num_bins
+        # Update the tallies' filter strides
+        other._update_filter_strides()
+        self._update_filter_strides()
 
         data = {}
         data['self'] = {}
@@ -1927,11 +1969,8 @@ class Tally(object):
         self.filters[filter1_index] = filter2
         self.filters[filter2_index] = filter1
 
-        # Update the strides for each of the filters
-        stride = self.num_nuclides * self.num_scores
-        for filter in reversed(self.filters):
-            filter.stride = stride
-            stride *= filter.num_bins
+        # Update the tally's filter strides
+        self._update_filter_strides()
 
         # Construct lists of tuples for the bins in each of the two filters
         filters = [filter1.type, filter2.type]
@@ -2449,8 +2488,8 @@ class Tally(object):
         if isinstance(power, Tally):
             new_tally = self.hybrid_product(power, binary_op='^')
 
-            # If original tally operands were sparse, sparsify the new tally
-            if self.sparse and other.sparse:
+            # If original tally operand was sparse, sparsify the new tally
+            if self.sparse:
                 new_tally.sparse = True
 
         elif isinstance(power, Real):
@@ -2708,11 +2747,8 @@ class Tally(object):
                 filter.bins = filter.bins[bin_indices]
                 filter.num_bins = num_bins
 
-        # Correct each Filter's stride
-        stride = new_tally.num_nuclides * new_tally.num_scores
-        for filter in reversed(new_tally.filters):
-            filter.stride = stride
-            stride *= filter.num_bins
+        # Update the new tally's filter strides
+        new_tally._update_filter_strides()
 
         # If original tally was sparse, sparsify the sliced tally
         new_tally.sparse = self.sparse
@@ -2758,69 +2794,107 @@ class Tally(object):
             A new tally which encapsulates the sum of data requested.
         """
 
-        # If user did not specify any scores, do not sum across scores
-        if len(scores) == 0:
-            scores = [[]]
-        # Sum across any scores specified by the user
-        else:
-            scores = [[score] for score in scores]
+        # Create new derived Tally for summation
+        tally_sum = Tally()
+        tally_sum._derived = True
+        tally_sum._estimator = self.estimator
+        tally_sum._num_realizations = self.num_realizations
+        tally_sum.with_batch_statistics = self.with_batch_statistics
+        tally_sum._with_summary = self.with_summary
+        tally_sum._sp_filename = self._sp_filename
+        tally_sum._results_read = self._results_read
 
-        # If user did not specify any nuclides, do not sum across nuclides
-        if len(nuclides) == 0:
-            nuclides = [[]]
-        # Sum across any nuclides specified by the user
-        else:
-            nuclides = [[nuclide] for nuclide in nuclides]
+        # Get tally data arrays reshaped with one dimension per filter
+        mean = self.get_reshaped_data(value='mean')
+        std_dev = self.get_reshaped_data(value='std_dev')
 
         # Sum across any filter bins specified by the user
         if filter_type in _FILTER_TYPES:
+            filter = self.find_filter(filter_type)
 
             # If user did not specify filter bins, sum across all bins
             if len(filter_bins) == 0:
-                filter = self.find_filter(filter_type)
-                if filter.type == 'distribcell':
-                    filter_bins = [[(i,)] for i in range(filter.num_bins)]
+                bin_indices = np.arange(filter.num_bins)
+
+                if filter_type == 'distribcell':
+                    filter_bins = np.arange(filter.num_bins)
                 else:
                     filter_bins = \
-                        [[(filter.get_bin(i),)] for i in range(filter.num_bins)]
+                        [(filter.get_bin(i)) for i in range(filter.num_bins)]
+
+            # Only sum across bins specified by the user
             else:
-                filter_bins = [[(filter_bin,)] for filter_bin in filter_bins]
+                bin_indices = \
+                    [filter.get_bin_index(i) for i in range(filter_bins)]
 
-            filters = [[filter_type]]
-        # If user did not specify a filter type, do not sum across filter bins
+            # Sum across the bins in the user-specified filter
+            for i, filter in enumerate(self.filters):
+                if filter.type == filter_type:
+                    mean = np.take(mean, indices=bin_indices, axis=i)
+                    std_dev = np.take(std_dev, indices=bin_indices, axis=i)
+                    mean = np.sum(mean, axis=i, keepdims=True)
+                    std_dev = np.sum(std_dev**2, axis=i, keepdims=True)
+                    std_dev = np.sqrt(std_dev)
+
+                    # Add AggregateFilter to the tally sum
+                    if not remove_filter:
+                        filter_sum = AggregateFilter(filter, filter_bins, 'sum')
+                        tally_sum.add_filter(filter_sum)
+
+                # Add a copy of each filter not summed across to the tally sum
+                else:
+                    tally_sum.add_filter(copy.deepcopy(filter))
+
+        # Add a copy of this tally's filters to the tally sum
         else:
-            filter_bins = [[]]
-            filters = [[]]
+            tally_sum._filters = copy.deepcopy(self.filters)
 
-        # Initialize Tally sum
-        tally_sum = 0
+        # Sum across any nuclides specified by the user
+        if len(nuclides) != 0:
+            nuclide_bins = [self.get_nuclide_index(nuclide) for nuclide in nuclides]
+            axis_index = len(self.filters)
+            mean = np.take(mean, indices=nuclide_bins, axis=axis_index)
+            std_dev = np.take(std_dev, indices=nuclide_bins, axis=axis_index)
+            mean = np.sum(mean, axis=axis_index, keepdims=True)
+            std_dev = np.sum(std_dev**2, axis=axis_index, keepdims=True)
+            std_dev = np.sqrt(std_dev)
 
-        # Iterate over all Tally slice operands in summation
-        prod = [scores, filters, filter_bins, nuclides]
-        summed_filters = defaultdict(list)
-        for scores, filters, filter_bins, nuclides in itertools.product(*prod):
-            tally_slice = self.get_slice(scores, filters, filter_bins, nuclides)
+            # Add AggregateNuclide to the tally sum
+            nuclide_sum = AggregateNuclide(nuclides, 'sum')
+            tally_sum.add_nuclide(nuclide_sum)
 
-            # Remove filters summed across to avoid bulky CrossFilters
-            if filter_type:
-                filter = tally_slice.find_filter(filter_type)
-                tally_slice.remove_filter(filter)
-                summed_filters[filter_type].append(filter)
-
-            # Accumulate this Tally slice into the Tally sum
-            tally_sum += tally_slice
-
-        # Add back the filter(s) which were summed across to derived tally,
-        # if filter bins were input; otherwise, leave out summed filter(s)
-        if remove_filter and filter_type is not None:
-            # Rename tally sum indicating a summation over a particular filter
-            tally_sum.name = 'sum({0}, {1})'.format(self.name, filter_type)
+        # Add a copy of this tally's nuclides to the tally sum
         else:
-            for summed_filter_type in summed_filters:
-                filters = summed_filters[summed_filter_type]
-                for i in range(1, len(filters)):
-                    filters[i] = CrossFilter(filters[i-1], filters[i], '+')
-                tally_sum.add_filter(filters[-1])
+            tally_sum._nuclides = copy.deepcopy(self.nuclides)
+
+        # Sum across any scores specified by the user
+        if len(scores) != 0:
+            score_bins = [self.get_score_index(score) for score in scores]
+            axis_index = self.num_nuclides + len(self.filters)
+            mean = np.take(mean, indices=score_bins, axis=axis_index)
+            std_dev = np.take(std_dev, indices=score_bins, axis=axis_index)
+            mean = np.sum(mean, axis=axis_index, keepdims=True)
+            std_dev = np.sum(std_dev**2, axis=axis_index, keepdims=True)
+            std_dev = np.sqrt(std_dev)
+
+            # Add AggregateScore to the tally sum
+            score_sum = AggregateScore(scores, 'sum')
+            tally_sum.add_score(score_sum)
+
+        # Add a copy of this tally's scores to the tally sum
+        else:
+            tally_sum._scores = copy.deepcopy(self.scores)
+
+        # Update the tally sum's filter strides
+        tally_sum._update_filter_strides()
+
+        # Reshape condensed data arrays with one dimension for all filters
+        mean = np.reshape(mean, tally_sum.shape)
+        std_dev = np.reshape(std_dev, tally_sum.shape)
+
+        # Assign tally sum's data with the new arrays
+        tally_sum._mean = mean
+        tally_sum._std_dev = std_dev
 
         # If original tally was sparse, sparsify the tally summation
         tally_sum.sparse = self.sparse
@@ -2887,11 +2961,8 @@ class Tally(object):
             new_tally._std_dev = np.zeros(new_tally.shape, dtype=np.float64)
             new_tally._std_dev[diag_indices, :, :] = self.std_dev
 
-        # Correct each Filter's stride
-        stride = new_tally.num_nuclides * new_tally.num_scores
-        for filter in reversed(new_tally.filters):
-            filter.stride = stride
-            stride *= filter.num_bins
+        # Update the new tally's filter strides
+        new_tally._update_filter_strides()
 
         # If original tally was sparse, sparsify the diagonalized tally
         new_tally.sparse = self.sparse