diff --git a/CMakeLists.txt b/CMakeLists.txt
index ba37925..c722255 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -23,9 +23,10 @@ if(SCRAN_AGGREGATE_FETCH_EXTERN)
     add_subdirectory(extern)
 else()
     find_package(tatami_tatami 3.0.0 CONFIG REQUIRED)
+    find_package(tatami_tatami_stats 1.1.0 CONFIG REQUIRED)
 endif()
 
-target_link_libraries(scran_aggregate INTERFACE tatami::tatami)
+target_link_libraries(scran_aggregate INTERFACE tatami::tatami tatami::tatami_stats)
 
 # Tests
 if(CMAKE_PROJECT_NAME STREQUAL PROJECT_NAME)
diff --git a/cmake/Config.cmake.in b/cmake/Config.cmake.in
index 8397be9..a236203 100644
--- a/cmake/Config.cmake.in
+++ b/cmake/Config.cmake.in
@@ -2,5 +2,6 @@
 
 include(CMakeFindDependencyMacro)
 find_dependency(tatami_tatami 3.0.0 CONFIG REQUIRED)
+find_dependency(tatami_tatami_stats 1.1.0 CONFIG REQUIRED)
 
 include("${CMAKE_CURRENT_LIST_DIR}/libscran_scran_aggregateTargets.cmake")
diff --git a/extern/CMakeLists.txt b/extern/CMakeLists.txt
index c7828fe..a34208d 100644
--- a/extern/CMakeLists.txt
+++ b/extern/CMakeLists.txt
@@ -6,4 +6,11 @@ FetchContent_Declare(
   GIT_TAG master # ^3.0.0
 )
 
+FetchContent_Declare(
+  tatami_stats
+  GIT_REPOSITORY https://github.com/tatami-inc/tatami_stats
+  GIT_TAG master # ^1.1.0
+)
+
 FetchContent_MakeAvailable(tatami)
+FetchContent_MakeAvailable(tatami_stats)
diff --git a/include/scran_aggregate/aggregate_across_cells.hpp b/include/scran_aggregate/aggregate_across_cells.hpp
index 749a9c8..99ac4d6 100644
--- a/include/scran_aggregate/aggregate_across_cells.hpp
+++ b/include/scran_aggregate/aggregate_across_cells.hpp
@@ -3,7 +3,9 @@
 
 #include <algorithm>
 #include <vector>
+
 #include "tatami/tatami.hpp"
+#include "tatami_stats/tatami_stats.hpp"
 
 /**
  * @file aggregate_across_cells.hpp
@@ -173,49 +175,68 @@ void compute_aggregate_by_column(
     tatami::Options opt;
     opt.sparse_ordered_index = false;
 
-    tatami::parallelize([&](size_t, Index_ s, Index_ l) {
+    tatami::parallelize([&](size_t t, Index_ s, Index_ l) {
         auto NC = p.ncol();
         auto ext = tatami::consecutive_extractor<sparse_>(&p, false, static_cast<Index_>(0), NC, s, l, opt);
         std::vector<Data_> vbuffer(l);
         typename std::conditional<sparse_, std::vector<Index_>, Index_>::type ibuffer(l);
 
+        size_t num_sums = buffers.sums.size();
+        std::vector<tatami_stats::LocalOutputBuffer<Sum_> > local_sums;
+        local_sums.reserve(num_sums);
+        for (auto ptr : buffers.sums) {
+            local_sums.emplace_back(t, s, l, ptr);
+        }
+        size_t num_detected = buffers.detected.size();
+        std::vector<tatami_stats::LocalOutputBuffer<Detected_> > local_detected;
+        local_detected.reserve(num_detected);
+        for (auto ptr : buffers.detected) {
+            local_detected.emplace_back(t, s, l, ptr);
+        }
+
         for (Index_ x = 0; x < NC; ++x) {
             auto current = factor[x];
 
             if constexpr(sparse_) {
                 auto col = ext->fetch(vbuffer.data(), ibuffer.data());
-                if (buffers.sums.size()) {
-                    auto& cursum = buffers.sums[current];
+                if (num_sums) {
+                    auto cursum = local_sums[current].data();
                     for (Index_ i = 0; i < col.number; ++i) {
-                        cursum[col.index[i]] += col.value[i];
+                        cursum[col.index[i] - s] += col.value[i];
                     }
                 }
 
-                if (buffers.detected.size()) {
-                    auto& curdetected = buffers.detected[current];
+                if (num_detected) {
+                    auto curdetected = local_detected[current].data();
                     for (Index_ i = 0; i < col.number; ++i) {
-                        curdetected[col.index[i]] += (col.value[i] > 0);
+                        curdetected[col.index[i] - s] += (col.value[i] > 0);
                     }
                 }
 
             } else {
                 auto col = ext->fetch(vbuffer.data());
-
-                if (buffers.sums.size()) {
-                    auto cursum = buffers.sums[current] + s;
+                if (num_sums) {
+                    auto cursum = local_sums[current].data();
                     for (Index_ i = 0; i < l; ++i) {
                         cursum[i] += col[i];
                     }
                 }
 
-                if (buffers.detected.size()) {
-                    auto curdetected = buffers.detected[current] + s;
+                if (num_detected) {
+                    auto curdetected = local_detected[current].data();
                     for (Index_ i = 0; i < l; ++i) {
                         curdetected[i] += (col[i] > 0);
                     }
                 }
             }
         }
+
+        for (auto& lsums : local_sums) {
+            lsums.transfer();
+        }
+        for (auto& ldetected : local_detected) {
+            ldetected.transfer();
+        }
     }, p.nrow(), options.num_threads);
 }
 
diff --git a/tests/src/aggregate_across_cells.cpp b/tests/src/aggregate_across_cells.cpp
index f5a2d88..9296eed 100644
--- a/tests/src/aggregate_across_cells.cpp
+++ b/tests/src/aggregate_across_cells.cpp
@@ -2,10 +2,11 @@
 
 #include "scran_aggregate/aggregate_across_cells.hpp"
 #include "scran_tests/scran_tests.hpp"
+
 #include <map>
 #include <random>
 
-std::vector<int> create_groupings(size_t n, int ngroups) {
+static std::vector<int> create_groupings(size_t n, int ngroups) {
     std::vector<int> groupings(n);
     for (size_t g = 0; g < groupings.size(); ++g) {
         groupings[g] = g % ngroups;
@@ -115,3 +116,51 @@ TEST(AggregateAcrossCells, Skipping) {
     EXPECT_EQ(skipped.sums.size(), 0);
     EXPECT_EQ(skipped.detected.size(), 0);
 }
+
+TEST(AggregateAcrossCells, DirtyBuffers) {
+    int nr = 88, nc = 126;
+    auto vec = scran_tests::simulate_vector(nr * nc, []{
+        scran_tests::SimulationParameters sparams;
+        sparams.density = 0.1;
+        sparams.seed = 69;
+        return sparams;
+    }());
+
+    tatami::DenseRowMatrix<double, int> dense_row(nr, nc, std::move(vec));
+    auto sparse_column = tatami::convert_to_compressed_sparse(&dense_row, false);
+    size_t ngroups = 3;
+    auto grouping = create_groupings(dense_row.ncol(), ngroups);
+
+    // Setting up some dirty buffers.
+    scran_aggregate::AggregateAcrossCellsResults<double, int> store;
+    scran_aggregate::AggregateAcrossCellsBuffers<double, int> buffers;
+    store.sums.resize(ngroups, std::vector<double>(nr, -1));
+    store.detected.resize(ngroups, std::vector<int>(nr, -1));
+    buffers.sums.resize(ngroups);
+    buffers.detected.resize(ngroups);
+    for (size_t l = 0; l < ngroups; ++l) {
+        buffers.sums[l] = store.sums[l].data();
+        buffers.detected[l] = store.detected[l].data();
+    }
+
+    scran_aggregate::AggregateAcrossCellsOptions opt;
+    auto ref = scran_aggregate::aggregate_across_cells(dense_row, grouping.data(), opt);
+    scran_aggregate::aggregate_across_cells(dense_row, grouping.data(), buffers, opt);
+    EXPECT_EQ(ref.sums.size(), store.sums.size());
+    EXPECT_EQ(ref.detected.size(), store.detected.size());
+    for (size_t l = 0; l < ngroups; ++l) {
+        EXPECT_EQ(ref.sums[l], store.sums[l]);
+        EXPECT_EQ(ref.detected[l], store.detected[l]);
+    }
+
+    // Same for column-major iteration.
+    for (size_t l = 0; l < ngroups; ++l) {
+        std::fill_n(buffers.sums[l], nr, -1);
+        std::fill_n(buffers.detected[l], nr, -1);
+    }
+    scran_aggregate::aggregate_across_cells(*sparse_column, grouping.data(), buffers, opt);
+    for (size_t l = 0; l < ngroups; ++l) {
+        EXPECT_EQ(ref.sums[l], store.sums[l]);
+        EXPECT_EQ(ref.detected[l], store.detected[l]);
+    }
+}