diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 3a5bd30..0c259cc 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -379,6 +379,19 @@
         dco = zlib.decompressobj()
         self.assertEqual(dco.flush(), b"") # Returns nothing
 
+    def test_decompress_incomplete_stream(self):
+        # This is 'foo', deflated
+        x = b'x\x9cK\xcb\xcf\x07\x00\x02\x82\x01E'
+        # For the record
+        self.assertEqual(zlib.decompress(x), b'foo')
+        self.assertRaises(zlib.error, zlib.decompress, x[:-5])
+        # Omitting the stream end works with decompressor objects
+        # (see issue #8672).
+        dco = zlib.decompressobj()
+        y = dco.decompress(x[:-5])
+        y += dco.flush()
+        self.assertEqual(y, b'foo')
+
     if hasattr(zlib.compressobj(), "copy"):
         def test_compresscopy(self):
             # Test copying a compression object
diff --git a/Misc/NEWS b/Misc/NEWS
index 491e0ac..66071eb 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -176,6 +176,10 @@
 Tests
 -----
 
+- Issue #8672: Add a zlib test ensuring that an incomplete stream can be
+  handled by a decompressor object without errors (it returns incomplete
+  uncompressed data).
+
 - Issue #8629: Disable some test_ssl tests, since they give different
   results with OpenSSL 1.0.0 and higher.