diff --git a/tests/test_tokenize.py b/tests/test_tokenize.py
index 6639f9a..594fe99 100644
--- a/tests/test_tokenize.py
+++ b/tests/test_tokenize.py
@@ -242,10 +242,27 @@
     assert tokenize.locate_tokens(input, filename) == located
 
 
+# Draws a token and possibly adds garbage
+@composite
+def draw_token_classified_garbled(draw):
+    token = draw(draw_token_classified())
+    value = token.value
+    type = token.type
+    if draw(booleans()):
+        value = draw(text(min_size=1)) + value
+        type = tokenize.TokenType.UNKNOWN
+    if draw(booleans()):
+        value = value + draw(text(min_size=1))
+        type = tokenize.TokenType.UNKNOWN
+    if value[0:2] == "#!":
+        type = tokenize.TokenType.SHEBANG
+    return tokenize.Token(value, token.location, type)
+
+
 # Generates a list of classified tokens and incorrectly classified tokens
 @composite
 def draw_tokens_classified(draw):
-    tokens = draw(lists(draw_token_classified()))
+    tokens = draw(lists(draw_token_classified_garbled()))
     input = []
     for t in tokens:
         type = draw(draw_token_type())
@@ -260,7 +277,7 @@
     assert tokenize.classify_tokens(input) == tokens
 
 
-# Draw random source code for fuzzing
+# Draw random source code that might be invalid for fuzzing
 @composite
 def draw_source_fuzz(draw):
     tokens = draw(lists(draw_token_classified()))