diff --git a/Doc/whatsnew/3.5.rst b/Doc/whatsnew/3.5.rst
index 3e44aa2..4530a13 100644
--- a/Doc/whatsnew/3.5.rst
+++ b/Doc/whatsnew/3.5.rst
@@ -393,6 +393,12 @@
   The *convert_charrefs* argument of :class:`~html.parser.HTMLParser` is
   now ``True`` by default (contributed by Berker Peksag in :issue:`21047`).
 
+* Although it is not formally part of the API, it is worth noting for porting
+  purposes (ie: fixing tests) that error messages that were previously of the
+  form "'sometype' does not support the buffer protocol" are now of the form "a
+  bytes-like object is required, not 'sometype'" (contributed by Ezio Melotti
+  in :issue:`16518`).
+
 Changes in the C API
 --------------------
 
diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 98ee615..3f2057b 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -711,11 +711,11 @@
         with self.assertRaises(TypeError) as cm:
             s.sendto('\u2620', sockname)
         self.assertEqual(str(cm.exception),
-                         "'str' does not support the buffer interface")
+                         "a bytes-like object is required, not 'str'")
         with self.assertRaises(TypeError) as cm:
             s.sendto(5j, sockname)
         self.assertEqual(str(cm.exception),
-                         "'complex' does not support the buffer interface")
+                         "a bytes-like object is required, not 'complex'")
         with self.assertRaises(TypeError) as cm:
             s.sendto(b'foo', None)
         self.assertIn('not NoneType',str(cm.exception))
@@ -723,11 +723,11 @@
         with self.assertRaises(TypeError) as cm:
             s.sendto('\u2620', 0, sockname)
         self.assertEqual(str(cm.exception),
-                         "'str' does not support the buffer interface")
+                         "a bytes-like object is required, not 'str'")
         with self.assertRaises(TypeError) as cm:
             s.sendto(5j, 0, sockname)
         self.assertEqual(str(cm.exception),
-                         "'complex' does not support the buffer interface")
+                         "a bytes-like object is required, not 'complex'")
         with self.assertRaises(TypeError) as cm:
             s.sendto(b'foo', 0, None)
         self.assertIn('not NoneType', str(cm.exception))
diff --git a/Misc/NEWS b/Misc/NEWS
index c23186d..3aa92e8 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -10,6 +10,10 @@
 Core and Builtins
 -----------------
 
+- Issue #16518: Use 'bytes-like object required' in error messages that
+  previously used the far more cryptic "'x' does not support the buffer
+  protocol.
+
 - Issue #22470: Fixed integer overflow issues in "backslashreplace",
   "xmlcharrefreplace", and "surrogatepass" error handlers.
 
diff --git a/Modules/_operator.c b/Modules/_operator.c
index 9c5c0d2..8f524a6 100644
--- a/Modules/_operator.c
+++ b/Modules/_operator.c
@@ -241,7 +241,7 @@
 "Return 'a == b'.  This function uses an approach designed to prevent\n"
 "timing analysis, making it appropriate for cryptography.\n"
 "a and b must both be of the same type: either str (ASCII only),\n"
-"or any type that supports the buffer protocol (e.g. bytes).\n"
+"or any bytes-like object.\n"
 "\n"
 "Note: If a and b are of different lengths, or if an error occurs,\n"
 "a timing attack could theoretically reveal information about the\n"
diff --git a/Objects/abstract.c b/Objects/abstract.c
index 177c34a..323c985 100644
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -260,8 +260,7 @@
     pb = obj->ob_type->tp_as_buffer;
     if (pb == NULL || pb->bf_getbuffer == NULL) {
         PyErr_SetString(PyExc_TypeError,
-                        "expected bytes, bytearray "
-                        "or buffer compatible object");
+                        "expected a bytes-like object");
         return -1;
     }
     if ((*pb->bf_getbuffer)(obj, &view, PyBUF_SIMPLE)) return -1;
@@ -306,7 +305,7 @@
     if (pb == NULL ||
         pb->bf_getbuffer == NULL) {
         PyErr_SetString(PyExc_TypeError,
-                        "expected an object with a buffer interface");
+                        "expected a bytes-like object");
         return -1;
     }
 
@@ -336,7 +335,7 @@
         pb->bf_getbuffer == NULL ||
         ((*pb->bf_getbuffer)(obj, &view, PyBUF_WRITABLE) != 0)) {
         PyErr_SetString(PyExc_TypeError,
-                        "expected an object with a writable buffer interface");
+                        "expected a writable bytes-like object");
         return -1;
     }
 
@@ -355,7 +354,7 @@
 {
     if (!PyObject_CheckBuffer(obj)) {
         PyErr_Format(PyExc_TypeError,
-                     "'%.100s' does not support the buffer interface",
+                     "a bytes-like object is required, not '%.100s'",
                      Py_TYPE(obj)->tp_name);
         return -1;
     }
@@ -530,8 +529,8 @@
     if (!PyObject_CheckBuffer(dest) ||
         !PyObject_CheckBuffer(src)) {
         PyErr_SetString(PyExc_TypeError,
-                        "both destination and source must have the "\
-                        "buffer interface");
+                        "both destination and source must be "\
+                        "bytes-like objects");
         return -1;
     }
 
diff --git a/Objects/bytearrayobject.c b/Objects/bytearrayobject.c
index f6f370d..84447bc 100644
--- a/Objects/bytearrayobject.c
+++ b/Objects/bytearrayobject.c
@@ -87,7 +87,7 @@
     if (buffer == NULL || buffer->bf_getbuffer == NULL)
     {
         PyErr_Format(PyExc_TypeError,
-                     "Type %.100s doesn't support the buffer API",
+                     "a bytes-like object is required, not '%.100s'",
                      Py_TYPE(obj)->tp_name);
         return -1;
     }
diff --git a/Objects/bytes_methods.c b/Objects/bytes_methods.c
index 5314ab4..1cf20c9 100644
--- a/Objects/bytes_methods.c
+++ b/Objects/bytes_methods.c
@@ -371,7 +371,7 @@
     if (buffer == NULL || buffer->bf_getbuffer == NULL)
     {
         PyErr_Format(PyExc_TypeError,
-                     "Type %.100s doesn't support the buffer API",
+                     "a bytes-like object is required, not '%.100s'",
                      Py_TYPE(obj)->tp_name);
         return -1;
     }
diff --git a/Objects/bytesobject.c b/Objects/bytesobject.c
index 87c0a25..ff99f93 100644
--- a/Objects/bytesobject.c
+++ b/Objects/bytesobject.c
@@ -29,7 +29,7 @@
     if (bufferprocs == NULL || bufferprocs->bf_getbuffer == NULL)
     {
         PyErr_Format(PyExc_TypeError,
-                     "Type %.100s doesn't support the buffer API",
+                     "a bytes-like object is required, not '%.100s'",
                      Py_TYPE(obj)->tp_name);
         return -1;
     }
diff --git a/Objects/longobject.c b/Objects/longobject.c
index bb2eb17..27bee50 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -4873,9 +4873,7 @@
 \n\
 Return the integer represented by the given array of bytes.\n\
 \n\
-The bytes argument must either support the buffer protocol or be an\n\
-iterable object producing bytes.  Bytes and bytearray are examples of\n\
-built-in objects that support the buffer protocol.\n\
+The bytes argument must be a bytes-like object (e.g. bytes or bytearray).\n\
 \n\
 The byteorder argument determines the byte order used to represent the\n\
 integer.  If byteorder is 'big', the most significant byte is at the\n\
diff --git a/Objects/memoryobject.c b/Objects/memoryobject.c
index 5148ce6..935da04 100644
--- a/Objects/memoryobject.c
+++ b/Objects/memoryobject.c
@@ -792,7 +792,7 @@
     }
 
     PyErr_Format(PyExc_TypeError,
-        "memoryview: %.200s object does not have the buffer interface",
+        "memoryview: a bytes-like object is required, not '%.200s'",
         Py_TYPE(v)->tp_name);
     return NULL;
 }
diff --git a/Python/getargs.c b/Python/getargs.c
index c749bb6..f7297da 100644
--- a/Python/getargs.c
+++ b/Python/getargs.c
@@ -1244,7 +1244,8 @@
            supports it directly. */
         if (PyObject_GetBuffer(arg, (Py_buffer*)p, PyBUF_WRITABLE) < 0) {
             PyErr_Clear();
-            return converterr("read-write buffer", arg, msgbuf, bufsize);
+            return converterr("read-write bytes-like object",
+                              arg, msgbuf, bufsize);
         }
         if (!PyBuffer_IsContiguous((Py_buffer*)p, 'C')) {
             PyBuffer_Release((Py_buffer*)p);
@@ -1282,7 +1283,7 @@
     *errmsg = NULL;
     *p = NULL;
     if (pb != NULL && pb->bf_releasebuffer != NULL) {
-        *errmsg = "read-only pinned buffer";
+        *errmsg = "read-only bytes-like object";
         return -1;
     }
 
@@ -1298,7 +1299,7 @@
 getbuffer(PyObject *arg, Py_buffer *view, char **errmsg)
 {
     if (PyObject_GetBuffer(arg, view, PyBUF_SIMPLE) != 0) {
-        *errmsg = "bytes or buffer";
+        *errmsg = "bytes-like object";
         return -1;
     }
     if (!PyBuffer_IsContiguous(view, 'C')) {