Eliminate outdated usages of PyInt_GetMax.
diff --git a/Doc/c-api/utilities.rst b/Doc/c-api/utilities.rst
index 0a92230..e3533f0 100644
--- a/Doc/c-api/utilities.rst
+++ b/Doc/c-api/utilities.rst
@@ -901,12 +901,10 @@
       Convert a C :ctype:`unsigned short int` to a Python integer object.
 
    ``I`` (integer/long) [unsigned int]
-      Convert a C :ctype:`unsigned int` to a Python integer object or a Python long
-      integer object, if it is larger than ``sys.maxint``.
+      Convert a C :ctype:`unsigned int` to a Python long integer object.
 
    ``k`` (integer/long) [unsigned long]
-      Convert a C :ctype:`unsigned long` to a Python integer object or a Python long
-      integer object, if it is larger than ``sys.maxint``.
+      Convert a C :ctype:`unsigned long` to a Python long integer object.
 
    ``L`` (long) [PY_LONG_LONG]
       Convert a C :ctype:`long long` to a Python integer object. Only available
diff --git a/Python/modsupport.c b/Python/modsupport.c
index aca57a4..68e1fa4 100644
--- a/Python/modsupport.c
+++ b/Python/modsupport.c
@@ -316,10 +316,7 @@
 		{
 			unsigned int n;
 			n = va_arg(*p_va, unsigned int);
-			if (n > (unsigned long)PyInt_GetMax())
-				return PyLong_FromUnsignedLong((unsigned long)n);
-			else
-				return PyLong_FromLong(n);
+			return PyLong_FromUnsignedLong(n);
 		}
 		
 		case 'n':
@@ -334,10 +331,7 @@
 		{
 			unsigned long n;
 			n = va_arg(*p_va, unsigned long);
-			if (n > (unsigned long)PyInt_GetMax())
-				return PyLong_FromUnsignedLong(n);
-			else
-				return PyLong_FromLong(n);
+			return PyLong_FromUnsignedLong(n);
 		}
 
 #ifdef HAVE_LONG_LONG