diff --git a/fairscale/optim/oss.py b/fairscale/optim/oss.py
index 18dce8c7a..26dfe7df2 100644
--- a/fairscale/optim/oss.py
+++ b/fairscale/optim/oss.py
@@ -5,7 +5,6 @@
 
 from collections import OrderedDict, deque
 import copy
-from enum import Enum, auto
 import itertools
 from itertools import chain
 import logging
@@ -27,11 +26,6 @@
     _params_t = Any
 
 
-class BucketFlush(Enum):
-    Reduce = auto()
-    Broadcast = auto()
-
-
 class OSS(Optimizer):
     """Wraps an arbitrary :class:`optim.Optimizer <torch.optim.Optimizer>`
     optimizer and shards its state as described by ZeRO_.
@@ -139,7 +133,16 @@ def partition_parameters(self) -> List[List[dict]]:
                     # Add this param to rank with smallest size.
                     rank = sizes.index(min(sizes))
                     param_lists[rank].append(param)
-                    sizes[rank] += param.numel()
+
+                    # We're partitioning the optimizer state,
+                    # so trainable parameters are the ones which really count
+                    if param.requires_grad:
+                        sizes[rank] += param.numel()
+                    else:
+                        # Spread frozen params on a per-tensor basis
+                        # Mostly useful for balance partitions for fine tuning for instance
+                        # Not required strictly speaking
+                        sizes[rank] += 1
 
                 for rank, params in enumerate(param_lists):
                     param_group_rank = copy.copy(param_group)
@@ -585,30 +588,6 @@ def _try_consume_work_handle(self) -> None:
             if work_handle.callback is not None:
                 work_handle.callback()
 
-    def _handle_trailing_buckets(self, flush_type: BucketFlush) -> None:
-        """
-        Go through the buckets, flush them if not already empty
-        .. warning: Could be that a bucket flush was already requested, needs to be handled carefully
-        """
-
-        for bucket_list in self.buckets.values():
-            for bucket in bucket_list:
-                if bucket.current_offset > 0:
-                    self.work_handles.append(
-                        Workhandle(
-                            handle=dist.broadcast(
-                                tensor=bucket.buffer, src=bucket.global_ref_rank, group=self.group, async_op=True,
-                            )
-                            if flush_type == BucketFlush.Broadcast
-                            else dist.reduce(
-                                tensor=bucket.buffer, dst=bucket.global_ref_rank, group=self.group, async_op=True,
-                            ),
-                            callback=bucket.unroll,
-                        )
-                    )
-
-        self._consume_work_handles()
-
     def _setup_bucket_strategy(self) -> None:
         """  Tag parameters to either bucket them or broadcast/reduce them directly. The parameters are ordered
         (smallest first), the bucket will hold the smallest elements, the remaining ones will be directly sent
diff --git a/tests/optim/test_oss.py b/tests/optim/test_oss.py
index e30a68427..13650fa59 100644
--- a/tests/optim/test_oss.py
+++ b/tests/optim/test_oss.py
@@ -178,16 +178,47 @@ def test_implicit_local_state_dict(self):
 
 def run_test_add_param_group(rank, world_size, tempfile_name):
     dist_init(rank, world_size, tempfile_name)
-    params = []
-    for size in [4, 5, 2, 6, 4]:
-        params.append(torch.rand(size, 1))
-    o = optim.OSS(params, lr=0.1)
-    assert len(o.param_groups) == 1
-    o.add_param_group({"params": [torch.rand(3, 1)]})
-    assert len(o.param_groups) == 2
-    # Verify that added group is added to the correct partition making all have 8 elements.
-    assert sum([x.numel() for g in o.optim.param_groups for x in g["params"]]) == 8
-    assert len(o.optim.param_groups) == 2
+
+    # Test with all parameters trainable to begin with
+    def all_trainable():
+        params = []
+        for size in [4, 5, 2, 6, 4]:
+            params.append(torch.rand(size, 1))
+
+        # Make sure that the params are trainable, enforces size-based partitioning
+        for p in params:
+            p.requires_grad = True
+
+        o = optim.OSS(params, lr=0.1)
+
+        assert len(o.param_groups) == 1
+        o.add_param_group({"params": [torch.rand(3, 1)]})
+
+        assert len(o.param_groups) == 2
+        # Verify that added group is added to the correct partition making all have 8 elements.
+        assert sum([x.numel() for g in o.optim.param_groups for x in g["params"]]) == 8
+        assert len(o.optim.param_groups) == 2
+
+    # Test a pathological config with a first big non-trainable param
+    def some_trainable():
+        params = []
+        for size in [100, 3, 5, 2, 6, 4]:
+            params.append(torch.rand(size, 1))
+
+        # Make sure that the params are trainable, enforces size-based partitioning
+        for p in params[1:]:
+            p.requires_grad = True
+
+        o = optim.OSS(params, lr=0.1)
+
+        assert len(o.param_groups) == 1
+        o.add_param_group({"params": [torch.rand(3, 1)]})
+
+        assert len(o.param_groups) == 2
+        assert len(o.optim.param_groups) == 2
+
+    all_trainable()
+    some_trainable()
 
     dist.destroy_process_group()
 
@@ -303,6 +334,11 @@ def run_test_sharding(rank, world_size, tempfile_name):
     params = []
     for size in [5, 4, 2, 6, 4, 3]:
         params.append(torch.rand(size, 1))
+
+    # Make sure that the params are trainable, enforces size-based partitioning
+    for p in params:
+        p.requires_grad = True
+
     o = optim.OSS(params, lr=0.1)
     assert sum([x.numel() for x in o.optim.param_groups[0]["params"]]) == 8