diff --git a/Include/longobject.h b/Include/longobject.h
index cd0cf308148..bcb93b9e2dd 100644
--- a/Include/longobject.h
+++ b/Include/longobject.h
@@ -84,6 +84,7 @@ PyAPI_FUNC(PyObject *) PyLong_FromString(char *, char **, int);
 #ifndef Py_LIMITED_API
 PyAPI_FUNC(PyObject *) PyLong_FromUnicode(Py_UNICODE*, Py_ssize_t, int);
 PyAPI_FUNC(PyObject *) PyLong_FromUnicodeObject(PyObject *u, int base);
+PyAPI_FUNC(PyObject *) _PyLong_FromBytes(const char *, Py_ssize_t, int);
 #endif
 
 #ifndef Py_LIMITED_API
diff --git a/Lib/test/test_int.py b/Lib/test/test_int.py
index 703c23312d4..c198bcc7401 100644
--- a/Lib/test/test_int.py
+++ b/Lib/test/test_int.py
@@ -73,14 +73,6 @@ class IntTestCases(unittest.TestCase):
         x = -1-sys.maxsize
         self.assertEqual(x >> 1, x//2)
 
-        self.assertRaises(ValueError, int, '123\0')
-        self.assertRaises(ValueError, int, '53', 40)
-
-        # SF bug 1545497: embedded NULs were not detected with
-        # explicit base
-        self.assertRaises(ValueError, int, '123\0', 10)
-        self.assertRaises(ValueError, int, '123\x00 245', 20)
-
         x = int('1' * 600)
         self.assertIsInstance(x, int)
 
@@ -360,14 +352,37 @@ class IntTestCases(unittest.TestCase):
                     int(TruncReturnsBadInt())
 
     def test_error_message(self):
-        testlist = ('\xbd', '123\xbd', '  123 456  ')
-        for s in testlist:
-            try:
-                int(s)
-            except ValueError as e:
-                self.assertIn(s.strip(), e.args[0])
-            else:
-                self.fail("Expected int(%r) to raise a ValueError", s)
+        def check(s, base=None):
+            with self.assertRaises(ValueError,
+                                   msg="int(%r, %r)" % (s, base)) as cm:
+                if base is None:
+                    int(s)
+                else:
+                    int(s, base)
+            self.assertEqual(cm.exception.args[0],
+                "invalid literal for int() with base %d: %r" %
+                (10 if base is None else base, s))
+
+        check('\xbd')
+        check('123\xbd')
+        check('  123 456  ')
+
+        check('123\x00')
+        # SF bug 1545497: embedded NULs were not detected with explicit base
+        check('123\x00', 10)
+        check('123\x00 245', 20)
+        check('123\x00 245', 16)
+        check('123\x00245', 20)
+        check('123\x00245', 16)
+        # byte string with embedded NUL
+        check(b'123\x00')
+        check(b'123\x00', 10)
+        # non-UTF-8 byte string
+        check(b'123\xbd')
+        check(b'123\xbd', 10)
+        # lone surrogate in Unicode string
+        check('123\ud800')
+        check('123\ud800', 10)
 
 def test_main():
     support.run_unittest(IntTestCases)
diff --git a/Misc/NEWS b/Misc/NEWS
index 00b5a69d86e..10d908cd6df 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,8 @@ What's New in Python 3.3.3 release candidate 1?
 Core and Builtins
 -----------------
 
+- Issue #16741: Fix an error reporting in int().
+
 - Issue #17899: Fix rare file descriptor leak in os.listdir().
 
 - Issue #18552: Check return value of PyArena_AddPyObject() in
diff --git a/Objects/abstract.c b/Objects/abstract.c
index 7c247243143..7f1808faea6 100644
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -1240,25 +1240,6 @@ convert_integral_to_int(PyObject *integral, const char *error_format)
 }
 
 
-/* Add a check for embedded NULL-bytes in the argument. */
-static PyObject *
-long_from_string(const char *s, Py_ssize_t len)
-{
-    char *end;
-    PyObject *x;
-
-    x = PyLong_FromString((char*)s, &end, 10);
-    if (x == NULL)
-        return NULL;
-    if (end != s + len) {
-        PyErr_SetString(PyExc_ValueError,
-                        "null byte in argument for int()");
-        Py_DECREF(x);
-        return NULL;
-    }
-    return x;
-}
-
 PyObject *
 PyNumber_Long(PyObject *o)
 {
@@ -1306,16 +1287,16 @@ PyNumber_Long(PyObject *o)
 
     if (PyBytes_Check(o))
         /* need to do extra error checking that PyLong_FromString()
-         * doesn't do.  In particular int('9.5') must raise an
-         * exception, not truncate the float.
+         * doesn't do.  In particular int('9\x005') must raise an
+         * exception, not truncate at the null.
          */
-        return long_from_string(PyBytes_AS_STRING(o),
-                                PyBytes_GET_SIZE(o));
+        return _PyLong_FromBytes(PyBytes_AS_STRING(o),
+                                 PyBytes_GET_SIZE(o), 10);
     if (PyUnicode_Check(o))
         /* The above check is done in PyLong_FromUnicode(). */
         return PyLong_FromUnicodeObject(o, 10);
     if (!PyObject_AsCharBuffer(o, &buffer, &buffer_len))
-        return long_from_string(buffer, buffer_len);
+        return _PyLong_FromBytes(buffer, buffer_len, 10);
 
     return type_error("int() argument must be a string or a "
                       "number, not '%.200s'", o);
diff --git a/Objects/longobject.c b/Objects/longobject.c
index d4dc45a23bc..30ffc94d416 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -2005,6 +2005,14 @@ long_from_binary_base(char **str, int base)
     return long_normalize(z);
 }
 
+/* Parses a long from a bytestring. Leading and trailing whitespace will be
+ * ignored.
+ *
+ * If successful, a PyLong object will be returned and 'pend' will be pointing
+ * to the first unused byte unless it's NULL.
+ *
+ * If unsuccessful, NULL will be returned.
+ */
 PyObject *
 PyLong_FromString(char *str, char **pend, int base)
 {
@@ -2267,12 +2275,17 @@ digit beyond the first.
         str++;
     if (*str != '\0')
         goto onError;
-    if (pend)
-        *pend = str;
     long_normalize(z);
-    return (PyObject *) maybe_small_long(z);
+    z = maybe_small_long(z);
+    if (z == NULL)
+        return NULL;
+    if (pend != NULL)
+        *pend = str;
+    return (PyObject *) z;
 
   onError:
+    if (pend != NULL)
+        *pend = str;
     Py_XDECREF(z);
     slen = strlen(orig_str) < 200 ? strlen(orig_str) : 200;
     strobj = PyUnicode_FromStringAndSize(orig_str, slen);
@@ -2285,6 +2298,31 @@ digit beyond the first.
     return NULL;
 }
 
+/* Since PyLong_FromString doesn't have a length parameter,
+ * check here for possible NULs in the string.
+ *
+ * Reports an invalid literal as a bytes object.
+ */
+PyObject *
+_PyLong_FromBytes(const char *s, Py_ssize_t len, int base)
+{
+    PyObject *result, *strobj;
+    char *end = NULL;
+
+    result = PyLong_FromString((char*)s, &end, base);
+    if (end == NULL || (result != NULL && end == s + len))
+        return result;
+    Py_XDECREF(result);
+    strobj = PyBytes_FromStringAndSize(s, Py_MIN(len, 200));
+    if (strobj != NULL) {
+        PyErr_Format(PyExc_ValueError,
+                     "invalid literal for int() with base %d: %R",
+                     base, strobj);
+        Py_DECREF(strobj);
+    }
+    return NULL;
+}
+
 PyObject *
 PyLong_FromUnicode(Py_UNICODE *u, Py_ssize_t length, int base)
 {
@@ -2299,9 +2337,8 @@ PyLong_FromUnicode(Py_UNICODE *u, Py_ssize_t length, int base)
 PyObject *
 PyLong_FromUnicodeObject(PyObject *u, int base)
 {
-    PyObject *result;
-    PyObject *asciidig;
-    char *buffer, *end;
+    PyObject *result, *asciidig, *strobj;
+    char *buffer, *end = NULL;
     Py_ssize_t buflen;
 
     asciidig = _PyUnicode_TransformDecimalAndSpaceToASCII(u);
@@ -2310,17 +2347,26 @@ PyLong_FromUnicodeObject(PyObject *u, int base)
     buffer = PyUnicode_AsUTF8AndSize(asciidig, &buflen);
     if (buffer == NULL) {
         Py_DECREF(asciidig);
-        return NULL;
+        if (!PyErr_ExceptionMatches(PyExc_UnicodeEncodeError))
+            return NULL;
     }
-    result = PyLong_FromString(buffer, &end, base);
-    if (result != NULL && end != buffer + buflen) {
-        PyErr_SetString(PyExc_ValueError,
-                        "null byte in argument for int()");
-        Py_DECREF(result);
-        result = NULL;
+    else {
+        result = PyLong_FromString(buffer, &end, base);
+        if (end == NULL || (result != NULL && end == buffer + buflen)) {
+            Py_DECREF(asciidig);
+            return result;
+        }
+        Py_DECREF(asciidig);
+        Py_XDECREF(result);
     }
-    Py_DECREF(asciidig);
-    return result;
+    strobj = PySequence_GetSlice(u, 0, 200);
+    if (strobj != NULL) {
+        PyErr_Format(PyExc_ValueError,
+                     "invalid literal for int() with base %d: %R",
+                     base, strobj);
+        Py_DECREF(strobj);
+    }
+    return NULL;
 }
 
 /* forward */
@@ -4308,23 +4354,12 @@ long_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
     if (PyUnicode_Check(x))
         return PyLong_FromUnicodeObject(x, (int)base);
     else if (PyByteArray_Check(x) || PyBytes_Check(x)) {
-        /* Since PyLong_FromString doesn't have a length parameter,
-         * check here for possible NULs in the string. */
         char *string;
-        Py_ssize_t size = Py_SIZE(x);
         if (PyByteArray_Check(x))
             string = PyByteArray_AS_STRING(x);
         else
             string = PyBytes_AS_STRING(x);
-        if (strlen(string) != (size_t)size || !size) {
-            /* We only see this if there's a null byte in x or x is empty,
-               x is a bytes or buffer, *and* a base is given. */
-            PyErr_Format(PyExc_ValueError,
-                         "invalid literal for int() with base %d: %R",
-                         (int)base, x);
-            return NULL;
-        }
-        return PyLong_FromString(string, NULL, (int)base);
+        return _PyLong_FromBytes(string, Py_SIZE(x), (int)base);
     }
     else {
         PyErr_SetString(PyExc_TypeError,