diff --git a/Doc/c-api/arg.rst b/Doc/c-api/arg.rst
index caceb40..f2bb8c6 100644
--- a/Doc/c-api/arg.rst
+++ b/Doc/c-api/arg.rst
@@ -206,7 +206,8 @@
    :c:func:`PyArg_ParseTuple` will use this location as the buffer and interpret the
    initial value of *\*buffer_length* as the buffer size.  It will then copy the
    encoded data into the buffer and NUL-terminate it.  If the buffer is not large
-   enough, a :exc:`ValueError` will be set.
+   enough, a :exc:`TypeError` will be set.
+   Note: starting from Python 3.6 a :exc:`ValueError` will be set.
 
    In both cases, *\*buffer_length* is set to the length of the encoded data
    without the trailing NUL byte.
diff --git a/Lib/test/test_capi.py b/Lib/test/test_capi.py
index 6a8685c..96666d1 100644
--- a/Lib/test/test_capi.py
+++ b/Lib/test/test_capi.py
@@ -489,7 +489,7 @@
                     format.encode("ascii"), keywords)
                 when_not_skipped = False
             except TypeError as e:
-                s = "argument 1 must be impossible<bad format char>, not int"
+                s = "argument 1 (impossible<bad format char>)"
                 when_not_skipped = (str(e) == s)
             except RuntimeError as e:
                 when_not_skipped = False
diff --git a/Python/getargs.c b/Python/getargs.c
index c365fc2..8aab067 100644
--- a/Python/getargs.c
+++ b/Python/getargs.c
@@ -342,7 +342,7 @@
                           flags, levels, msgbuf,
                           sizeof(msgbuf), &freelist);
         if (msg) {
-            seterror(i+1, msg, levels, fname, msg);
+            seterror(i+1, msg, levels, fname, message);
             return cleanreturn(0, &freelist);
         }
     }
@@ -535,9 +535,15 @@
 {
     assert(expected != NULL);
     assert(arg != NULL);
-    PyOS_snprintf(msgbuf, bufsize,
-                  "must be %.50s, not %.50s", expected,
-                  arg == Py_None ? "None" : arg->ob_type->tp_name);
+    if (expected[0] == '(') {
+        PyOS_snprintf(msgbuf, bufsize,
+                      "%.100s", expected);
+    }
+    else {
+        PyOS_snprintf(msgbuf, bufsize,
+                      "must be %.50s, not %.50s", expected,
+                      arg == Py_None ? "None" : arg->ob_type->tp_name);
+    }
     return msgbuf;
 }
 
@@ -741,7 +747,7 @@
         if (PyLong_Check(arg))
             ival = PyLong_AsUnsignedLongMask(arg);
         else
-            return converterr("integer<k>", arg, msgbuf, bufsize);
+            return converterr("int", arg, msgbuf, bufsize);
         *p = ival;
         break;
     }
@@ -766,7 +772,7 @@
         if (PyLong_Check(arg))
             ival = PyLong_AsUnsignedLongLongMask(arg);
         else
-            return converterr("integer<K>", arg, msgbuf, bufsize);
+            return converterr("int", arg, msgbuf, bufsize);
         *p = ival;
         break;
     }
@@ -1123,9 +1129,11 @@
             } else {
                 if (size + 1 > BUFFER_LEN) {
                     Py_DECREF(s);
-                    return converterr(
-                        "(buffer overflow)",
-                        arg, msgbuf, bufsize);
+                    PyErr_Format(PyExc_TypeError,
+                                 "encoded string too long "
+                                 "(%zd, maximum length %zd)",
+                                 (Py_ssize_t)size, (Py_ssize_t)(BUFFER_LEN-1));
+                    RETURN_ERR_OCCURRED;
                 }
             }
             memcpy(*buffer, ptr, size+1);
@@ -1147,7 +1155,7 @@
             if ((Py_ssize_t)strlen(ptr) != size) {
                 Py_DECREF(s);
                 return converterr(
-                    "encoded string without NULL bytes",
+                    "encoded string without null bytes",
                     arg, msgbuf, bufsize);
             }
             *buffer = PyMem_NEW(char, size + 1);
@@ -1237,7 +1245,7 @@
 
         if (*format != '*')
             return converterr(
-                "invalid use of 'w' format character",
+                "(invalid use of 'w' format character)",
                 arg, msgbuf, bufsize);
         format++;
 
@@ -1261,7 +1269,7 @@
     }
 
     default:
-        return converterr("impossible<bad format char>", arg, msgbuf, bufsize);
+        return converterr("(impossible<bad format char>)", arg, msgbuf, bufsize);
 
     }