diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 9137f8a..1b802b8 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -134,6 +134,18 @@
         x = zlib.compress(data)
         self.assertEqual(zlib.decompress(x), data)
 
+    def test_incomplete_stream(self):
+        # An useful error message is given
+        x = zlib.compress(HAMLET_SCENE)
+        try:
+            zlib.decompress(x[:-1])
+        except zlib.error as e:
+            self.assertTrue(
+                "Error -5 while decompressing data: incomplete or truncated stream"
+                in str(e), str(e))
+        else:
+            self.fail("zlib.error not raised")
+
     # Memory use of the following functions takes into account overallocation
 
     @precisionbigmemtest(size=_1G + 1024 * 1024, memuse=3)
diff --git a/Misc/NEWS b/Misc/NEWS
index 46e5737..a95371a 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -39,6 +39,9 @@
 Library
 -------
 
+- Issue #8681: Make the zlib module's error messages more informative when
+  the zlib itself doesn't give any detailed explanation.
+
 - Issue #8674: Fixed a number of incorrect or undefined-behaviour-inducing
   overflow checks in the audioop module.
 
diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
index bb52fdc..183f01e 100644
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -72,10 +72,24 @@
 static void
 zlib_error(z_stream zst, int err, char *msg)
 {
-    if (zst.msg == Z_NULL)
+    const char *zmsg = zst.msg;
+    if (zmsg == Z_NULL) {
+        switch (err) {
+        case Z_BUF_ERROR:
+            zmsg = "incomplete or truncated stream";
+            break;
+        case Z_STREAM_ERROR:
+            zmsg = "inconsistent stream state";
+            break;
+        case Z_DATA_ERROR:
+            zmsg = "invalid input data";
+            break;
+        }
+    }
+    if (zmsg == Z_NULL)
         PyErr_Format(ZlibError, "Error %d %s", err, msg);
     else
-        PyErr_Format(ZlibError, "Error %d %s: %.200s", err, msg, zst.msg);
+        PyErr_Format(ZlibError, "Error %d %s: %.200s", err, msg, zmsg);
 }
 
 PyDoc_STRVAR(compressobj__doc__,
@@ -248,8 +262,7 @@
              * process the inflate call() due to an error in the data.
              */
             if (zst.avail_out > 0) {
-                PyErr_Format(ZlibError, "Error %i while decompressing data",
-                             err);
+                zlib_error(zst, err, "while decompressing data");
                 inflateEnd(&zst);
                 goto error;
             }