diff --git a/outlines/generate/api.py b/outlines/generate/api.py
index e8afa526d..edf4d0fbb 100644
--- a/outlines/generate/api.py
+++ b/outlines/generate/api.py
@@ -318,6 +318,9 @@ def stream(
         if isinstance(stop_at, str):
             stop_at = [stop_at]
 
+        if max_words and max_tokens is None:
+            max_tokens = 3 * max_words
+
         stop_sequences = stop_at
         num_samples = self.num_samples
 
diff --git a/tests/generate/test_generator.py b/tests/generate/test_generator.py
index 4a7e7da1f..f83ee62b7 100644
--- a/tests/generate/test_generator.py
+++ b/tests/generate/test_generator.py
@@ -536,8 +536,11 @@ def __call__(self, biased_logits, *_):
             return torch.argmax(biased_logits, keepdims=True), torch.tensor([0]), None
 
     generator = SequenceGenerator(MockFSM(), MockModel(), sampler(), "cpu")
-    result = generator("test", max_words=5)
-    assert result == "test test test test test"
+    result = generator("test", max_words=3)
+    assert result == "test test test"
+
+    sequence = generator.stream("test", max_words=3)
+    assert "".join(sequence) == "test test test"
 
 
 def test_generator_max_tokens_from_max_words():
@@ -583,3 +586,6 @@ def __call__(self, biased_logits, *_):
     generator = SequenceGenerator(MockFSM(), MockModel(), sampler(), "cpu")
     result = generator("test", max_words=2)  # should generate max_words * 3 tokens
     assert result == "123456"
+
+    sequence = generator.stream("test", max_words=2)
+    assert "".join(sequence) == "123456"