diff --git a/mergekit/merge_methods/generalized_task_arithmetic.py b/mergekit/merge_methods/generalized_task_arithmetic.py
index 2bfbcd74..55ad5a2b 100644
--- a/mergekit/merge_methods/generalized_task_arithmetic.py
+++ b/mergekit/merge_methods/generalized_task_arithmetic.py
@@ -49,6 +49,7 @@ def parameters(self) -> List[ConfigParameterDef]:
             ConfigParameterDef(
                 name="rescale", required=False, default_value=self.default_rescale
             ),
+            ConfigParameterDef(name="adjusted", required=False, default_value=False),
         ]
 
     def tensor_parameters(self) -> List[ConfigParameterDef]:
@@ -73,6 +74,7 @@ def make_task(
             int8_mask=parameters["int8_mask"],
             normalize=parameters["normalize"],
             rescale=parameters["rescale"],
+            adjusted=parameters["adjusted"],
             out_tensor_name=output_weight.name,
         )
 
@@ -86,6 +88,7 @@ class GTATask(Task[torch.Tensor]):
     int8_mask: bool
     normalize: bool
     rescale: bool
+    adjusted: bool
 
     def uses_accelerator(self) -> bool:
         return True
@@ -116,6 +119,7 @@ def execute(
                     density=tv_info["density"],
                     method=self.method.sparsification_method,
                     rescale=self.rescale,
+                    adjusted=self.adjusted,
                 )
 
         deltas = torch.stack([tv["delta"] for tv in tvs], dim=0)
diff --git a/mergekit/sparsify.py b/mergekit/sparsify.py
index 69c923ac..e8b106be 100644
--- a/mergekit/sparsify.py
+++ b/mergekit/sparsify.py
@@ -59,7 +59,7 @@ def magnitude(tensor: torch.Tensor, density: float, rescale: bool) -> torch.Tens
     return res
 
 
-def bernoulli(tensor: torch.Tensor, density: float, rescale: bool) -> torch.Tensor:
+def bernoulli(tensor: torch.Tensor, density: float, rescale: bool, adjusted: bool) -> torch.Tensor:
     if density >= 1:
         return tensor
 
@@ -69,6 +69,12 @@ def bernoulli(tensor: torch.Tensor, density: float, rescale: bool) -> torch.Tens
         # torch.bernoulli not implemented for float16 on CPU, upcast to float32
         work_dtype = torch.float32
 
+    if adjusted:
+        s = (tensor.count_nonzero() / tensor.numel()).item()
+        if density >= s:
+            return tensor
+        density /= s
+
     mask = torch.bernoulli(
         torch.full_like(input=tensor, fill_value=density, dtype=work_dtype)
     )
@@ -83,10 +89,11 @@ def sparsify(
     density: float,
     method: SparsificationMethod,
     rescale: bool = False,
+    adjusted: bool = False,
 ) -> torch.Tensor:
     if method == SparsificationMethod.magnitude:
         return magnitude(tensor, density=density, rescale=rescale)
     elif method == SparsificationMethod.random:
-        return bernoulli(tensor, density=density, rescale=rescale)
+        return bernoulli(tensor, density=density, rescale=rescale, adjusted=adjusted)
     else:
         raise NotImplementedError(method)