diff --git a/optillm/entropy_decoding.py b/optillm/entropy_decoding.py
index 3a768fc..201f313 100644
--- a/optillm/entropy_decoding.py
+++ b/optillm/entropy_decoding.py
@@ -63,16 +63,16 @@ def _sample(logits: torch.Tensor, temperature=0.666, top_p=0.90, top_k=27, min_p
     probs = F.softmax(logit / temperature, dim=-1)
 
     if min_p > 0.0:
+        # Drop tokens below min_p times the most likely token's probability
         p_max = torch.max(probs, dim=-1, keepdim=True).values
-        indices_to_remove = probs < (min_p * p_max)
-        logit = torch.where(indices_to_remove, torch.full_like(logit, float('-inf')), logit)
+        probs = probs.masked_fill(probs < (min_p * p_max), 0.0)
 
-    top_k_probs, top_k_indices = torch.topk(probs, k=min(top_k, probs.shape[-1]))
-    probs_sort = torch.flip(top_k_probs, dims=[-1])
-    probs_idx = torch.flip(top_k_indices, dims=[-1])
+    # Nucleus over the top-k tokens in descending order: keep each token until
+    # the probability of the tokens before it exceeds top_p, which always
+    # keeps the most likely token and removes the least likely tail.
+    probs_sort, probs_idx = torch.topk(probs, k=min(top_k, probs.shape[-1]))
     probs_sum = torch.cumsum(probs_sort, dim=-1)
-    mask = torch.where(probs_sum - probs_sort > top_p, torch.tensor(1.0, device=device), torch.tensor(0.0, device=device))
-    probs_sort = probs_sort * (1 - mask)
+    probs_sort = probs_sort.masked_fill(probs_sum - probs_sort > top_p, 0.0)
     probs_sort = probs_sort / torch.sum(probs_sort, dim=-1, keepdim=True)
     next_token = torch.multinomial(probs_sort, 1, generator=generator)
     next_token_g = torch.gather(probs_idx, -1, next_token.reshape(bsz, 1).to(torch.int64))
diff --git a/tests/test_entropy_decoding_sampling.py b/tests/test_entropy_decoding_sampling.py
new file mode 100644
index 0000000..6483b5a
--- /dev/null
+++ b/tests/test_entropy_decoding_sampling.py
@@ -0,0 +1,33 @@
+"""Offline regression tests for top-p and min-p filtering in entropy decoding."""
+
+import torch
+
+from optillm.entropy_decoding import _sample
+
+
+def sampled_tokens(probs, num_samples=2000, **kwargs):
+    logits = probs.log().view(1, 1, -1)
+    generator = torch.Generator().manual_seed(0)
+    return {
+        _sample(logits, generator=generator, **kwargs).item()
+        for _ in range(num_samples)
+    }
+
+
+def test_top_p_keeps_the_most_likely_token():
+    # The 39 less likely tokens together exceed top_p.
+    probs = torch.tensor([0.05] + [0.95 / 39] * 39)
+
+    tokens = sampled_tokens(probs, temperature=1.0, top_p=0.9, top_k=40)
+
+    assert 0 in tokens
+    # The nucleus keeps tokens until those before them exceed 0.9: 36 of 40.
+    assert tokens == set(range(36))
+
+
+def test_min_p_removes_unlikely_tokens():
+    probs = torch.tensor([0.5, 0.3] + [0.2 / 20] * 20)
+
+    tokens = sampled_tokens(probs, temperature=1.0, top_p=1.0, top_k=22, min_p=0.1)
+
+    assert tokens == {0, 1}