diff --git a/Lib/test/string_tests.py b/Lib/test/string_tests.py
index cd3ee48a92..d36ae0c298 100644
--- a/Lib/test/string_tests.py
+++ b/Lib/test/string_tests.py
@@ -1140,6 +1140,24 @@ class MixinStrUnicodeUserStringTest:
         # but either raises a MemoryError, or succeeds (if you have 54TiB)
         #self.checkraises(OverflowError, 10000*'abc', '__mul__', 2000000000)
 
+    @support.cpython_only
+    def test_mul_c_limits(self):
+        from _testcapi import PY_SSIZE_T_MAX, PY_SSIZE_T_MIN
+
+        # the following tests also test sequence_repeat in Objects/abstract.c
+        self.checkraises(OverflowError, '', '__mul__', -1 << 1000)
+        self.checkraises(OverflowError, '', '__mul__', PY_SSIZE_T_MIN - 1)
+        self.checkequal('', 'a', '__mul__', PY_SSIZE_T_MIN)
+        self.checkequal('', '', '__mul__', PY_SSIZE_T_MAX)
+        self.checkraises(OverflowError, '', '__mul__', PY_SSIZE_T_MAX + 1)
+        self.checkraises(OverflowError, '', '__mul__', 1 << 1000)
+
+        # result's length can't be bigger than PY_SSIZE_T_MAX
+        self.checkraises(OverflowError,
+                         'ab', '__mul__', PY_SSIZE_T_MAX // 2 + 1)
+        self.checkraises(OverflowError,
+                         'ab' * 0x1000, '__mul__', PY_SSIZE_T_MAX)
+
     def test_join(self):
         # join now works with any sequence type
         # moved here, because the argument order is
diff --git a/Lib/test/test_stat.py b/Lib/test/test_stat.py
index cd02a6ee37..7baa1c781c 100644
--- a/Lib/test/test_stat.py
+++ b/Lib/test/test_stat.py
@@ -1,7 +1,8 @@
 import unittest
 import os
 import sys
-from test.support import TESTFN, import_fresh_module, android_not_root
+from test.support import (TESTFN, import_fresh_module, android_not_root,
+                          cpython_only)
 
 c_stat = import_fresh_module('stat', fresh=['_stat'])
 py_stat = import_fresh_module('stat', blocked=['_stat'])
@@ -223,6 +224,26 @@ class TestFilemodeCStat(TestFilemode, unittest.TestCase):
     format_funcs = TestFilemode.format_funcs | {'S_ISDOOR', 'S_ISPORT',
                                                 'S_ISWHT'}
 
+    @cpython_only
+    def test_mode_t_converter(self):
+        # test _PyLong_AsMode_t by testing S_IMODE, which uses
+        # _PyLong_AsMode_t to convert the argument it receives.
+        self.assertRaises(TypeError, c_stat.S_IMODE, 1.0)
+        self.assertRaises(TypeError, c_stat.S_IMODE, '1')
+
+        self.assertRaises(OverflowError, c_stat.S_IMODE, -1 << 1000)
+        self.assertRaises(OverflowError, c_stat.S_IMODE, -1)
+        c_stat.S_IMODE(0)
+        self.assertRaises(OverflowError, c_stat.S_IMODE, 1 << 1000)
+
+    @cpython_only
+    @unittest.skipUnless(sys.platform == "win32", 'Windows-specific test')
+    def test_mode_t_converter_windows(self):
+        from _testcapi import USHRT_MAX
+
+        c_stat.S_IMODE(USHRT_MAX) # verify OverflowError is not raised
+        self.assertRaises(OverflowError, c_stat.S_IMODE, USHRT_MAX + 1)
+
 
 class TestFilemodePyStat(TestFilemode, unittest.TestCase):
     statmod = py_stat
diff --git a/Modules/_ctypes/callproc.c b/Modules/_ctypes/callproc.c
index 9b368caf65..e55da5b1bb 100644
--- a/Modules/_ctypes/callproc.c
+++ b/Modules/_ctypes/callproc.c
@@ -650,7 +650,8 @@ static int ConvParam(PyObject *obj, Py_ssize_t index, struct argument *pa)
             pa->value.i = PyLong_AsLong(obj);
             if (pa->value.i == -1 && PyErr_Occurred()) {
                 PyErr_SetString(PyExc_OverflowError,
-                                "int too long to convert");
+                                "Python int fits neither C unsigned long nor "
+                                "C long");
                 return -1;
             }
         }
diff --git a/Modules/_cursesmodule.c b/Modules/_cursesmodule.c
index 4d714cecdf..0b70a53353 100644
--- a/Modules/_cursesmodule.c
+++ b/Modules/_cursesmodule.c
@@ -244,6 +244,8 @@ PyCurses_ConvertToChtype(PyCursesWindowObject *win, PyObject *obj, chtype *ch)
     else if (PyLong_CheckExact(obj)) {
         int long_overflow;
         value = PyLong_AsLongAndOverflow(obj, &long_overflow);
+        /* PyLong_Check(obj) is true, so it is guaranteed that
+           no error occurred in PyLong_AsLongAndOverflow. */
         if (long_overflow)
             goto overflow;
     }
@@ -260,7 +262,7 @@ PyCurses_ConvertToChtype(PyCursesWindowObject *win, PyObject *obj, chtype *ch)
 
 overflow:
     PyErr_SetString(PyExc_OverflowError,
-                    "byte doesn't fit in chtype");
+                    "Python object does not fit in C chtype");
     return 0;
 }
 
@@ -309,9 +311,11 @@ PyCurses_ConvertToCchar_t(PyCursesWindowObject *win, PyObject *obj,
     else if (PyLong_CheckExact(obj)) {
         int overflow;
         value = PyLong_AsLongAndOverflow(obj, &overflow);
+        /* PyLong_Check(obj) is true, so it is guaranteed that
+           no error occurred in PyLong_AsLongAndOverflow. */
         if (overflow) {
             PyErr_SetString(PyExc_OverflowError,
-                            "int doesn't fit in long");
+                            "Python int does not fit in C chtype");
             return 0;
         }
     }
@@ -325,7 +329,7 @@ PyCurses_ConvertToCchar_t(PyCursesWindowObject *win, PyObject *obj,
     *ch = (chtype)value;
     if ((long)*ch != value) {
         PyErr_Format(PyExc_OverflowError,
-                     "byte doesn't fit in chtype");
+                     "Python object does not fit in C chtype");
         return 0;
     }
     return 1;
@@ -2591,7 +2595,7 @@ PyCurses_KeyName(PyObject *self, PyObject *args)
     if (!PyArg_ParseTuple(args,"i",&ch)) return NULL;
 
     if (ch < 0) {
-        PyErr_SetString(PyExc_ValueError, "invalid key number");
+        PyErr_SetString(PyExc_ValueError, "key number must be non-negative");
         return NULL;
     }
     knp = keyname(ch);
@@ -3089,15 +3093,17 @@ PyCurses_ConvertToWchar_t(PyObject *obj,
         long value;
         int overflow;
         value = PyLong_AsLongAndOverflow(obj, &overflow);
+        /* PyLong_Check(obj) is true, so it is guaranteed that
+           no error occurred in PyLong_AsLongAndOverflow. */
         if (overflow) {
             PyErr_SetString(PyExc_OverflowError,
-                            "int doesn't fit in long");
+                            "Python int does not fit in C wchar_t");
             return 0;
         }
         *wch = (wchar_t)value;
         if ((long)*wch != value) {
             PyErr_Format(PyExc_OverflowError,
-                         "character doesn't fit in wchar_t");
+                         "Python int does not fit in C wchar_t");
             return 0;
         }
         return 1;
diff --git a/Modules/_stat.c b/Modules/_stat.c
index f6cb303500..12ff9d0822 100644
--- a/Modules/_stat.c
+++ b/Modules/_stat.c
@@ -251,12 +251,18 @@ _PyLong_AsMode_t(PyObject *op)
     mode_t mode;
 
     value = PyLong_AsUnsignedLong(op);
-    if ((value == (unsigned long)-1) && PyErr_Occurred())
+    if ((value == (unsigned long)-1) && PyErr_Occurred()) {
+        if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
+            PyErr_SetString(PyExc_OverflowError,
+                            "Python int does not fit in C mode_t");
+        }
         return (mode_t)-1;
+    }
 
     mode = (mode_t)value;
     if ((unsigned long)mode != value) {
-        PyErr_SetString(PyExc_OverflowError, "mode out of range");
+        PyErr_SetString(PyExc_OverflowError,
+                        "Python int does not fit in C mode_t");
         return (mode_t)-1;
     }
     return mode;
diff --git a/Objects/abstract.c b/Objects/abstract.c
index 4a75b92e1d..8b89ea4bef 100644
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -936,8 +936,14 @@ sequence_repeat(ssizeargfunc repeatfunc, PyObject *seq, PyObject *n)
     Py_ssize_t count;
     if (PyIndex_Check(n)) {
         count = PyNumber_AsSsize_t(n, PyExc_OverflowError);
-        if (count == -1 && PyErr_Occurred())
+        if (count == -1 && PyErr_Occurred()) {
+            if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
+                PyErr_SetString(PyExc_OverflowError,
+                                "sequence repeat count does not fit in C "
+                                "Py_ssize_t");
+            }
             return NULL;
+        }
     }
     else {
         return type_error("can't multiply sequence by "