diff --git a/src/DataStructures/DataBox/DataBox.hpp b/src/DataStructures/DataBox/DataBox.hpp
index 5b12b6c0f5b90..f59d42eba3c07 100644
--- a/src/DataStructures/DataBox/DataBox.hpp
+++ b/src/DataStructures/DataBox/DataBox.hpp
@@ -559,8 +559,19 @@ std::map<std::string, size_t> DataBox<tmpl::list<Tags...>>::size_of_items()
     (void)this;
     using tag = tmpl::type_from<decltype(tag_v)>;
     if constexpr (not db::is_reference_tag_v<tag>) {
-      const auto& item = get_item<tag>();
-      result[pretty_type::get_name<tag>()] = size_of_object_in_bytes(item);
+      // For item of ItemType::Compute, this will not evaluate its function
+      // (i.e. if the item has never been evaluated its size will be that of a
+      // default initialized object)
+      const auto& item = get_item<tag>().get();
+      if constexpr (tt::is_a_v<std::unique_ptr, typename tag::type>) {
+        if (item == nullptr) {
+          result[pretty_type::get_name<tag>()] = 0;
+        } else {
+          result[pretty_type::get_name<tag>()] = size_of_object_in_bytes(*item);
+        }
+      } else {
+        result[pretty_type::get_name<tag>()] = size_of_object_in_bytes(item);
+      }
     }
   };
   tmpl::for_each<mutable_item_creation_tags>(add_item_size);
diff --git a/src/ParallelAlgorithms/Events/ObserveDataBox.hpp b/src/ParallelAlgorithms/Events/ObserveDataBox.hpp
index 1ee7afffd5a0e..601396dd07d01 100644
--- a/src/ParallelAlgorithms/Events/ObserveDataBox.hpp
+++ b/src/ParallelAlgorithms/Events/ObserveDataBox.hpp
@@ -53,7 +53,7 @@ struct ReduceDataBoxSize {
     auto& observer_writer_proxy = Parallel::get_parallel_component<
         observers::ObserverWriter<Metavariables>>(cache);
     const std::string subfile_name =
-        "/ObserveDataBox/" + pretty_type::name<ContributingComponent>();
+        "/DataBoxSizeInMb/" + pretty_type::name<ContributingComponent>();
     std::vector<std::string> legend;
     legend.reserve(item_sizes.size() + 1);
     legend.emplace_back("Time");
@@ -95,6 +95,13 @@ struct ContributeDataBoxSize {
 };
 }  // namespace detail
 
+/// \brief Event that will collect the size in MBs used by each DataBox item on
+/// each parallel component.
+///
+/// \details The data will be written to disk in the reductions file under the
+/// `/DataBoxSizeInMb/` group. The name of each file is the `pretty_type::name`
+/// of each parallel component.  There will be a column for each item in the
+/// DataBox that is not a subitem or reference item.
 class ObserveDataBox : public Event {
  public:
   /// \cond
diff --git a/tests/Unit/DataStructures/DataBox/Test_DataBox.cpp b/tests/Unit/DataStructures/DataBox/Test_DataBox.cpp
index 2f57332972ebf..baf7a5a54d253 100644
--- a/tests/Unit/DataStructures/DataBox/Test_DataBox.cpp
+++ b/tests/Unit/DataStructures/DataBox/Test_DataBox.cpp
@@ -3269,9 +3269,36 @@ void test_output() {
   CHECK(item_size.at("(anonymous namespace)::test_databox_tags::Tag1") == 32);
   CHECK(item_size.at("(anonymous namespace)::test_databox_tags::Tag2") == 24);
   CHECK(item_size.at("(anonymous namespace)::test_databox_tags::Tag4Compute") ==
-        9);
+        8);
   CHECK(item_size.at("(anonymous namespace)::test_databox_tags::Tag5Compute") ==
-        29);
+        28);
+
+  const auto box_with_ptrs =
+      db::create<db::AddSimpleTags<test_databox_tags::Pointer>,
+                 db::AddComputeTags<test_databox_tags::PointerToCounterCompute,
+                                    test_databox_tags::PointerToSumCompute>>(
+          std::make_unique<int>(3));
+  const auto item_size_ptrs = box_with_ptrs.size_of_items();
+  CHECK(item_size_ptrs.size() == 3);
+  CHECK(item_size_ptrs.at(
+            "(anonymous namespace)::test_databox_tags::Pointer") == 4);
+  CHECK(item_size_ptrs.at(
+            "(anonymous "
+            "namespace)::test_databox_tags::PointerToCounterCompute") == 0);
+  CHECK(item_size_ptrs.at(
+            "(anonymous namespace)::test_databox_tags::PointerToSumCompute") ==
+        0);
+  db::get<test_databox_tags::PointerToSumCompute>(box_with_ptrs);
+  const auto item_size_ptrs_after = box_with_ptrs.size_of_items();
+  CHECK(item_size_ptrs_after.size() == 3);
+  CHECK(item_size_ptrs_after.at(
+            "(anonymous namespace)::test_databox_tags::Pointer") == 4);
+  CHECK(item_size_ptrs_after.at(
+            "(anonymous "
+            "namespace)::test_databox_tags::PointerToCounterCompute") == 4);
+  CHECK(item_size_ptrs_after.at(
+            "(anonymous namespace)::test_databox_tags::PointerToSumCompute") ==
+        4);
 }
 
 void test_exception_safety() {