diff --git a/benchmarks/oss.py b/benchmarks/oss.py
index 281239a3d..63905e725 100755
--- a/benchmarks/oss.py
+++ b/benchmarks/oss.py
@@ -5,7 +5,7 @@
 import math
 import os
 import time
-from typing import Any, List
+from typing import Any, List, Union, cast
 
 import torch
 import torch.distributed as dist
@@ -19,6 +19,7 @@
 from fairscale.optim.oss import OSS
 
 BACKEND = dist.Backend.NCCL if torch.cuda.is_available() else dist.Backend.GLOO  # type: ignore
+OPTIM = torch.optim.RMSprop
 
 
 def dist_init(rank, world_size):
@@ -36,7 +37,9 @@ def train(
     use_oss: bool = True,
     check_regression: bool = True,
     reference_speed: float = -1.0,
+    reference_memory: float = -1.0,
 ):
+
     # DDP
     dist_init(rank, world_size)
 
@@ -50,21 +53,18 @@ def collate(inputs: List[Any]):
             "label": torch.stack([i[1] for i in inputs]).to(rank),
         }
 
-    def print_(msg):
-        if dist.get_rank() == 0:
-            print(msg)
-
     dataloader = DataLoader(
         dataset=FakeData(transform=ToTensor(), size=data_size), batch_size=batch_size, collate_fn=collate
     )
     loss_fn = nn.CrossEntropyLoss()
 
+    # Reset the memory use counter
+    torch.cuda.reset_peak_memory_stats(rank)
+
     # Shard the optimizer
-    optimizer = (
-        OSS(params=model.parameters(), optim=torch.optim.SGD, lr=1e-4, momentum=0.9)
-        if use_oss
-        else torch.optim.SGD(model.parameters(), lr=1e-4, momentum=0.9)
-    )
+    optimizer: Union[OSS, OPTIM] = OSS(
+        params=model.parameters(), optim=OPTIM, lr=1e-4, momentum=0.9
+    ) if use_oss else OPTIM(model.parameters(), lr=1e-4, momentum=0.9)
 
     # Dummy training loop
     torch.cuda.synchronize(rank)
@@ -90,8 +90,19 @@ def closure():
             optimizer.step(closure)
 
         epoch_end = time.monotonic()
+
+        if use_oss:
+            # Check the checkpointing in the case of the OSS optimizer
+            # Memory usage could spill over from there
+            optimizer = cast(OSS, optimizer)
+            # optimizer.consolidate_state_dict()
+            if dist.get_rank() == 0:
+                # _ = optimizer.state_dict()
+                print("... State dict collected")
+
         measurements.append(data_size / (epoch_end - epoch_start))
-        print_(f"Epoch {epoch} - processed {measurements[-1]:.2f} img per sec")
+        if dist.get_rank() == 0:
+            print(f"Epoch {epoch} - processed {measurements[-1]:.2f} img per sec")
 
     torch.cuda.synchronize(rank)
     training_stop = time.monotonic()
@@ -101,13 +112,15 @@ def closure():
     print(f"[{dist.get_rank()}] : Training done. {img_per_sec:.2f} img per sec overall")
     print(f"[{dist.get_rank()}] : Peak memory {max_memory:.1f}MiB")
 
+    # Compute the mean and average img per second
+    mean = sum(measurements) / len(measurements)
+    diff = map(lambda x: pow(x - mean, 2.0), measurements)
+    std = math.sqrt(sum(diff) / (len(measurements) - 1))
+    print(f"[{dist.get_rank()}] : Mean speed: {mean:.2f} +/- {std:.2f}")
+
     if use_oss and check_regression and dist.get_rank() == 0:
-        # Compute the mean and average img per second
-        mean = sum(measurements) / len(measurements)
-        diff = map(lambda x: pow(x - mean, 2.0), measurements)
-        std = math.sqrt(sum(diff) / (len(measurements) - 1))
-        print(f"[Regression Test] Mean: {mean:.2f} +/- {std:.2f}")
-        assert (mean - 3.0 * std) < reference_speed, "Regression detected"
+        assert (mean - 3.0 * std) < reference_speed, "Speed regression detected"
+        assert max_memory < 1.05 * reference_memory, "Memory use regression detected"
         print("[Regression Test] VALID")
 
 
@@ -122,10 +135,11 @@ def closure():
     parser.add_argument("--data_size", action="store", default=512, type=int)
     parser.add_argument("--check_regression", action="store", default=True, type=bool)
     parser.add_argument("--reference_speed", action="store", default=39.82, type=float)
+    parser.add_argument("--reference_memory", action="store", default=4475, type=float)
 
     args = parser.parse_args()
 
-    print("\nBenchmark vanilla SGD")
+    print("\nBenchmark vanilla optimizer")
     mp.spawn(
         train,
         args=(args.world_size, args.epochs, args.batch_size, args.data_size, False, False),
@@ -144,6 +158,7 @@ def closure():
             True,
             args.check_regression,
             args.reference_speed,
+            args.reference_memory,
         ),
         nprocs=args.world_size,
         join=True,