diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
index c78cf42..c0dd7cd 100644
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -560,17 +560,22 @@
         Py_END_ALLOW_THREADS
     }
 
-    /* Not all of the compressed data could be accommodated in the output buffer
-       of specified size. Return the unconsumed tail in an attribute.*/
     if(max_length) {
+        /* Not all of the compressed data could be accommodated in a buffer of
+           the specified size. Return the unconsumed tail in an attribute. */
         Py_DECREF(self->unconsumed_tail);
         self->unconsumed_tail = PyBytes_FromStringAndSize((char *)self->zst.next_in,
                                                            self->zst.avail_in);
-        if(!self->unconsumed_tail) {
-            Py_DECREF(RetVal);
-            RetVal = NULL;
-            goto error;
-        }
+    }
+    else if (PyBytes_GET_SIZE(self->unconsumed_tail) > 0) {
+        /* All of the compressed data was consumed. Clear unconsumed_tail. */
+        Py_DECREF(self->unconsumed_tail);
+        self->unconsumed_tail = PyBytes_FromStringAndSize("", 0);
+    }
+    if (self->unconsumed_tail == NULL) {
+        Py_DECREF(RetVal);
+        RetVal = NULL;
+        goto error;
     }
 
     /* The end of the compressed data has been reached, so set the