diff --git a/include/openmc/cell.h b/include/openmc/cell.h
index 201c1e5bc..ef454c6e8 100644
--- a/include/openmc/cell.h
+++ b/include/openmc/cell.h
@@ -44,6 +44,7 @@ constexpr int32_t OP_UNION        {std::numeric_limits<int32_t>::max() - 4};
 //==============================================================================
 
 class Cell;
+class ParentCell;
 class CellInstance;
 class Universe;
 class UniversePartitioner;
@@ -151,13 +152,15 @@ public:
 
   //! Get all cell instances contained by this cell
   //! \return Map with cell indexes as keys and instances as values
-  std::unordered_map<int32_t, std::set<int32_t>>
+  std::unordered_map<int32_t, std::vector<int32_t>>
   get_contained_cells();
 
+protected:
   void
-  get_contained_cells_inner(std::unordered_map<int32_t, std::set<int32_t>>& contained_cells,
-                            std::vector<CellInstance>& parent_cells);
+  get_contained_cells_inner(std::unordered_map<int32_t, std::vector<int32_t>>& contained_cells,
+                            std::vector<ParentCell>& parent_cells);
 
+public:
   //----------------------------------------------------------------------------
   // Data members
 
@@ -307,6 +310,16 @@ private:
   std::vector<std::vector<int32_t>> partitions_;
 };
 
+
+//==============================================================================
+//! Define a containing (parent) cell
+//==============================================================================
+
+struct ParentCell {
+  gsl::index cell_index;
+  gsl::index lattice_index;
+};
+
 //==============================================================================
 //! Define an instance of a particular cell
 //==============================================================================
diff --git a/src/cell.cpp b/src/cell.cpp
index 3217f2031..08476d31f 100644
--- a/src/cell.cpp
+++ b/src/cell.cpp
@@ -1175,10 +1175,10 @@ openmc_cell_set_name(int32_t index, const char* name) {
 }
 
 
-std::unordered_map<int32_t, std::set<int32_t>>
+std::unordered_map<int32_t, std::vector<int32_t>>
 Cell::get_contained_cells() {
-  std::unordered_map<int32_t, std::set<int32_t>> contained_cells;
-  std::vector<CellInstance> parent_cells;
+  std::unordered_map<int32_t, std::vector<int32_t>> contained_cells;
+  std::vector<ParentCell> parent_cells;
 
   this->get_contained_cells_inner(contained_cells, parent_cells);
 
@@ -1187,8 +1187,8 @@ Cell::get_contained_cells() {
 
 //! Get all cells within this cell
 void
-Cell::get_contained_cells_inner(std::unordered_map<int32_t, std::set<int32_t>>& contained_cells,
-                                std::vector<CellInstance>& parent_cells)
+Cell::get_contained_cells_inner(std::unordered_map<int32_t, std::vector<int32_t>>& contained_cells,
+                                std::vector<ParentCell>& parent_cells)
 {
 
   // filled by material, determine instance based on parent cells
@@ -1196,18 +1196,19 @@ Cell::get_contained_cells_inner(std::unordered_map<int32_t, std::set<int32_t>>&
     int instance = 0;
     if (this->distribcell_index_ >= 0) {
       for (int i = 0; i < parent_cells.size(); i++) {
-        auto& cell = model::cells[parent_cells[i].index_cell];
+        auto& cell = model::cells[parent_cells[i].cell_index];
         if (cell->type_ == Fill::UNIVERSE) {
           instance += cell->offset_[this->distribcell_index_];
         } else if (cell->type_ == Fill::LATTICE) {
           auto& lattice = model::lattices[cell->fill_];
-          instance += lattice->offset(this->distribcell_index_, parent_cells[i].instance);
+          instance += lattice->offset(this->distribcell_index_, parent_cells[i].lattice_index);
         }
       }
     }
     // add entry to contained cells
-    contained_cells[model::cell_map[this->id_]].insert(instance);
-  // filled with universe, add the containing cell and recurse
+    contained_cells[model::cell_map[this->id_]].push_back(instance);
+  // filled with universe, add the containing cell to the parent cells
+  // and recurse
   } else if (this->type_ == Fill::UNIVERSE) {
     parent_cells.push_back({model::cell_map[this->id_], -1});
     auto& univ = model::universes[fill_];
@@ -1217,7 +1218,7 @@ Cell::get_contained_cells_inner(std::unordered_map<int32_t, std::set<int32_t>>&
     }
     parent_cells.pop_back();
   // filled with a lattice, visit each universe in the lattice
-  // with a recursive call
+  // with a recursive call to collect the cell instances
   } else if (this->type_ == Fill::LATTICE) {
     auto& lattice = model::lattices[this->fill_];
     for (auto i = lattice->begin(); i != lattice->end(); ++i) {