diff --git a/fi/include/reverse_purge_hash_map_impl.hpp b/fi/include/reverse_purge_hash_map_impl.hpp
index fa84c9e6..73fb803e 100644
--- a/fi/include/reverse_purge_hash_map_impl.hpp
+++ b/fi/include/reverse_purge_hash_map_impl.hpp
@@ -353,8 +353,9 @@ V reverse_purge_hash_map<K, V, H, E, A>::purge() {
   const uint32_t limit = std::min(MAX_SAMPLE_SIZE, num_active_);
   uint32_t num_samples = 0;
   uint32_t i = 0;
-  AllocV av(allocator_);
-  V* samples = av.allocate(limit);
+  // A temporary of at most MAX_SAMPLE_SIZE values: on the stack rather than from the allocator, which need not be
+  // able to give memory back (e.g. an arena)
+  V samples[MAX_SAMPLE_SIZE];
   while (num_samples < limit) {
     if (is_active(i)) {
       samples[num_samples++] = values_[i];
@@ -363,7 +364,6 @@ V reverse_purge_hash_map<K, V, H, E, A>::purge() {
   }
   std::nth_element(samples, samples+ (num_samples / 2), samples + num_samples);
   const V median = samples[num_samples / 2];
-  av.deallocate(samples, limit);
   subtract_and_keep_positive_only(median);
   return median;
 }
diff --git a/fi/test/frequent_items_sketch_custom_type_test.cpp b/fi/test/frequent_items_sketch_custom_type_test.cpp
index 6d077da4..85e0d6ba 100644
--- a/fi/test/frequent_items_sketch_custom_type_test.cpp
+++ b/fi/test/frequent_items_sketch_custom_type_test.cpp
@@ -98,4 +98,35 @@ TEST_CASE("frequent items: negative weight", "[frequent_items_sketch]") {
   REQUIRE(test_allocator_total_bytes == 0);
 }
 
+// An allocator that counts its allocate() calls.
+static long long counting_allocations = 0;
+
+template<typename T>
+struct counting_allocator {
+  using value_type = T;
+  counting_allocator() = default;
+  template<typename U>
+  counting_allocator(const counting_allocator<U>&) {}
+  T* allocate(std::size_t n) {
+    ++counting_allocations;
+    return static_cast<T*>(::operator new(n * sizeof(T)));
+  }
+  void deallocate(T* p, std::size_t) { ::operator delete(p); }
+};
+template<typename T, typename U>
+bool operator==(const counting_allocator<T>&, const counting_allocator<U>&) { return true; }
+template<typename T, typename U>
+bool operator!=(const counting_allocator<T>&, const counting_allocator<U>&) { return false; }
+
+TEST_CASE("frequent items: a purge does not allocate", "[frequent_items_sketch]") {
+  using sketch = frequent_items_sketch<int, uint64_t, std::hash<int>, std::equal_to<int>, counting_allocator<int>>;
+  // start the map at its maximum size, so it never grows and only purges
+  sketch s(5, 5);
+  for (int i = 0; i < 1000; ++i) s.update(i);
+  const long long before = counting_allocations;
+  for (int i = 1000; i < 100000; ++i) s.update(i); // thousands of purges
+  REQUIRE(counting_allocations == before);
+  REQUIRE(s.get_total_weight() == 100000);
+}
+
 } /* namespace datasketches */