diff --git a/src/core/lib/surface/channel.c b/src/core/lib/surface/channel.c
index d6c7aee40d8..b4bfb92042d 100644
--- a/src/core/lib/surface/channel.c
+++ b/src/core/lib/surface/channel.c
@@ -194,8 +194,14 @@ grpc_channel *grpc_channel_create(grpc_exec_ctx *exec_ctx, const char *target,
 
 size_t grpc_channel_get_call_size_estimate(grpc_channel *channel) {
 #define ROUND_UP_SIZE 256
+  /* We round up our current estimate to the NEXT value of ROUND_UP_SIZE.
+     This ensures:
+      1. a consistent size allocation when our estimate is drifting slowly
+         (which is common) - which tends to help most allocators reuse memory
+      2. a small amount of allowed growth over the estimate without hitting
+         the arena size doubling case, reducing overall memory usage */
   return ((size_t)gpr_atm_no_barrier_load(&channel->call_size_estimate) +
-          ROUND_UP_SIZE) &
+          2 * ROUND_UP_SIZE) &
          ~(size_t)(ROUND_UP_SIZE - 1);
 }
 
diff --git a/test/core/memory_usage/client.c b/test/core/memory_usage/client.c
index 107abbc1b3d..51ea51bc12f 100644
--- a/test/core/memory_usage/client.c
+++ b/test/core/memory_usage/client.c
@@ -237,6 +237,11 @@ int main(int argc, char **argv) {
       0, grpc_slice_from_static_string("Reflector/GetAfterSvrCreation"));
 
   // warmup period
+  for (int i = 0; i < warmup_iterations; i++) {
+    send_snapshot_request(
+        0, grpc_slice_from_static_string("Reflector/SimpleSnapshot"));
+  }
+
   for (call_idx = 0; call_idx < warmup_iterations; ++call_idx) {
     init_ping_pong_request(call_idx + 1);
   }