diff --git a/Modules/cPickle.c b/Modules/cPickle.c
index b87f4983f21..c61035d57b4 100644
--- a/Modules/cPickle.c
+++ b/Modules/cPickle.c
@@ -68,6 +68,20 @@ static char cPickle_module_documentation[] =
 
 #define WRITE_BUF_SIZE 256
 
+/* --------------------------------------------------------------------------
+NOTES on format codes.
+XXX much more is needed here
+
+Integer types
+BININT1		8-bit unsigned integer; followed by 1 byte.
+BININT2         16-bit unsigned integer; followed by 2 bytes, little-endian.
+BININT		32-bit signed integer; followed by 4 bytes, little-endian.
+INT		Integer; natural decimal string conversion, then newline.
+                CAUTION:  INT-reading code can't assume that what follows
+                fits in a Python int, because the size of Python ints varies
+                across platforms.
+LONG		Long (unbounded) integer; repr(i), then newline.
+-------------------------------------------------------------------------- */
 
 #define MARK        '('
 #define STOP        '.'
@@ -904,18 +918,20 @@ save_int(Picklerobject *self, PyObject *args) {
 
     if (!self->bin
 #if SIZEOF_LONG > 4
-        || (l >> 32)
+        || l >  0x7fffffffL
+        || l < -0x80000000L
 #endif
-            ) {
-                /* Save extra-long ints in non-binary mode, so that
-                   we can use python long parsing code to restore,
-                   if necessary. */
+       ) {
+        /* Text-mode pickle, or long too big to fit in the 4-byte
+         * signed BININT format:  store as a string.
+         */
         c_str[0] = INT;
         sprintf(c_str + 1, "%ld\n", l);
         if ((*self->write_func)(self, c_str, strlen(c_str)) < 0)
             return -1;
     }
     else {
+    	/* Binary pickle and l fits in a signed 4-byte int. */
         c_str[1] = (int)( l        & 0xff);
         c_str[2] = (int)((l >> 8)  & 0xff);
         c_str[3] = (int)((l >> 16) & 0xff);