diff --git a/Include/longintrepr.h b/Include/longintrepr.h
index df157a8..c32d72c 100644
--- a/Include/longintrepr.h
+++ b/Include/longintrepr.h
@@ -19,14 +19,13 @@
    long_pow() requires that SHIFT be divisible by 5. */
 
 typedef unsigned short digit;
-typedef unsigned int wdigit; /* digit widened to parameter size */
 #define BASE_TWODIGITS_TYPE long
 typedef unsigned BASE_TWODIGITS_TYPE twodigits;
 typedef BASE_TWODIGITS_TYPE stwodigits; /* signed variant of twodigits */
 
 #define PyLong_SHIFT    15
 #define PyLong_BASE     ((digit)1 << PyLong_SHIFT)
-#define PyLong_MASK     ((int)(PyLong_BASE - 1))
+#define PyLong_MASK     ((digit)(PyLong_BASE - 1))
 
 /* b/w compatibility with Python 2.5 */
 #define SHIFT	PyLong_SHIFT
diff --git a/Lib/test/test_sys.py b/Lib/test/test_sys.py
index bd819c6..128880d 100644
--- a/Lib/test/test_sys.py
+++ b/Lib/test/test_sys.py
@@ -593,12 +593,12 @@
         # listreverseiterator (list)
         check(reversed([]), size(h + 'lP'))
         # long
-        check(0L, size(vh + 'H') - self.H)
-        check(1L, size(vh + 'H'))
-        check(-1L, size(vh + 'H'))
-        check(32768L, size(vh + 'H') + self.H)
-        check(32768L*32768L-1, size(vh + 'H') + self.H)
-        check(32768L*32768L, size(vh + 'H') + 2*self.H)
+        check(0L, size(vh))
+        check(1L, size(vh) + self.H)
+        check(-1L, size(vh) + self.H)
+        check(32768L, size(vh) + 2*self.H)
+        check(32768L*32768L-1, size(vh) + 2*self.H)
+        check(32768L*32768L, size(vh) + 3*self.H)
         # module
         check(unittest, size(h + 'P'))
         # None
diff --git a/Misc/NEWS b/Misc/NEWS
index e1778df..142026c 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,10 @@
 Core and Builtins
 -----------------
 
+- Issue #5260: Long integers now consume less memory:  average
+  saving is 2 bytes per long on a 32-bit system and 6 bytes per long
+  on a 64-bit system.
+
 - Issue #5186: Reduce hash collisions for objects with no __hash__ method by
   rotating the object pointer by 4 bits to the right.
 
diff --git a/Objects/longobject.c b/Objects/longobject.c
index ddfa72b..af222de 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -8,6 +8,7 @@
 #include "longintrepr.h"
 
 #include <ctype.h>
+#include <stddef.h>
 
 /* For long multiplication, use the O(N**2) school algorithm unless
  * both operands contain more than KARATSUBA_CUTOFF digits (this
@@ -30,12 +31,6 @@
 #define MAX(x, y) ((x) < (y) ? (y) : (x))
 #define MIN(x, y) ((x) > (y) ? (y) : (x))
 
-/* Forward */
-static PyLongObject *long_normalize(PyLongObject *);
-static PyLongObject *mul1(PyLongObject *, wdigit);
-static PyLongObject *muladd1(PyLongObject *, wdigit, wdigit);
-static PyLongObject *divrem1(PyLongObject *, digit, digit *);
-
 #define SIGCHECK(PyTryBlock) \
 	if (--_Py_Ticker < 0) { \
 		_Py_Ticker = _Py_CheckInterval; \
@@ -62,16 +57,20 @@
 /* Allocate a new long int object with size digits.
    Return NULL and set exception if we run out of memory. */
 
+#define MAX_LONG_DIGITS \
+	((PY_SSIZE_T_MAX - offsetof(PyLongObject, ob_digit))/sizeof(digit))
+
 PyLongObject *
 _PyLong_New(Py_ssize_t size)
 {
-	if (size > PY_SSIZE_T_MAX) {
-		PyErr_NoMemory();
+	if (size > MAX_LONG_DIGITS) {
+		PyErr_SetString(PyExc_OverflowError,
+				"too many digits in integer");
 		return NULL;
 	}
 	/* coverity[ampersand_in_size] */
-	/* XXX(nnorwitz): This can overflow --
-           PyObject_NEW_VAR / _PyObject_VAR_SIZE need to detect overflow */
+	/* XXX(nnorwitz): PyObject_NEW_VAR / _PyObject_VAR_SIZE need to detect
+	   overflow */
 	return PyObject_NEW_VAR(PyLongObject, &PyLong_Type, size);
 }
 
@@ -197,8 +196,8 @@
 		return NULL;
 	frac = ldexp(frac, (expo-1) % PyLong_SHIFT + 1);
 	for (i = ndig; --i >= 0; ) {
-		long bits = (long)frac;
-		v->ob_digit[i] = (digit) bits;
+		digit bits = (digit)frac;
+		v->ob_digit[i] = bits;
 		frac = frac - (double)bits;
 		frac = ldexp(frac, PyLong_SHIFT);
 	}
@@ -438,9 +437,9 @@
 	int incr;			/* direction to move pstartbyte */
 	const unsigned char* pendbyte;	/* MSB of bytes */
 	size_t numsignificantbytes;	/* number of bytes that matter */
-	size_t ndigits;			/* number of Python long digits */
+	Py_ssize_t ndigits;		/* number of Python long digits */
 	PyLongObject* v;		/* result */
-	int idigit = 0;  		/* next free index in v->ob_digit */
+	Py_ssize_t idigit = 0;		/* next free index in v->ob_digit */
 
 	if (n == 0)
 		return PyLong_FromLong(0L);
@@ -483,12 +482,16 @@
 	}
 
 	/* How many Python long digits do we need?  We have
-	   8*numsignificantbytes bits, and each Python long digit has PyLong_SHIFT
-	   bits, so it's the ceiling of the quotient. */
+	   8*numsignificantbytes bits, and each Python long digit has
+	   PyLong_SHIFT bits, so it's the ceiling of the quotient. */
+	/* catch overflow before it happens */
+	if (numsignificantbytes > (PY_SSIZE_T_MAX - PyLong_SHIFT) / 8) {
+		PyErr_SetString(PyExc_OverflowError,
+				"byte array too long to convert to int");
+		return NULL;
+	}
 	ndigits = (numsignificantbytes * 8 + PyLong_SHIFT - 1) / PyLong_SHIFT;
-	if (ndigits > (size_t)INT_MAX)
-		return PyErr_NoMemory();
-	v = _PyLong_New((int)ndigits);
+	v = _PyLong_New(ndigits);
 	if (v == NULL)
 		return NULL;
 
@@ -517,8 +520,9 @@
 			accumbits += 8;
 			if (accumbits >= PyLong_SHIFT) {
 				/* There's enough to fill a Python digit. */
-				assert(idigit < (int)ndigits);
-				v->ob_digit[idigit] = (digit)(accum & PyLong_MASK);
+				assert(idigit < ndigits);
+				v->ob_digit[idigit] = (digit)(accum &
+							      PyLong_MASK);
 				++idigit;
 				accum >>= PyLong_SHIFT;
 				accumbits -= PyLong_SHIFT;
@@ -527,7 +531,7 @@
 		}
 		assert(accumbits < PyLong_SHIFT);
 		if (accumbits) {
-			assert(idigit < (int)ndigits);
+			assert(idigit < ndigits);
 			v->ob_digit[idigit] = (digit)accum;
 			++idigit;
 		}
@@ -1124,19 +1128,11 @@
 /* Multiply by a single digit, ignoring the sign. */
 
 static PyLongObject *
-mul1(PyLongObject *a, wdigit n)
-{
-	return muladd1(a, n, (digit)0);
-}
-
-/* Multiply by a single digit and add a single digit, ignoring the sign. */
-
-static PyLongObject *
-muladd1(PyLongObject *a, wdigit n, wdigit extra)
+mul1(PyLongObject *a, digit n)
 {
 	Py_ssize_t size_a = ABS(Py_SIZE(a));
 	PyLongObject *z = _PyLong_New(size_a+1);
-	twodigits carry = extra;
+	twodigits carry = 0;
 	Py_ssize_t i;
 
 	if (z == NULL)
@@ -1757,8 +1753,6 @@
 static PyLongObject *x_divrem
 	(PyLongObject *, PyLongObject *, PyLongObject **);
 static PyObject *long_long(PyObject *v);
-static int long_divrem(PyLongObject *, PyLongObject *,
-	PyLongObject **, PyLongObject **);
 
 /* Long division with remainder, top-level routine */
 
@@ -1976,14 +1970,12 @@
 		sign = -1;
 		i = -(i);
 	}
-#define LONG_BIT_PyLong_SHIFT	(8*sizeof(long) - PyLong_SHIFT)
 	/* The following loop produces a C unsigned long x such that x is
 	   congruent to the absolute value of v modulo ULONG_MAX.  The
 	   resulting x is nonzero if and only if v is. */
 	while (--i >= 0) {
 		/* Force a native long #-bits (32 or 64) circular shift */
-		x = ((x << PyLong_SHIFT) & ~PyLong_MASK) |
-			((x >> LONG_BIT_PyLong_SHIFT) & PyLong_MASK);
+		x = (x >> (8*SIZEOF_LONG-PyLong_SHIFT)) | (x << PyLong_SHIFT);
 		x += v->ob_digit[i];
 		/* If the addition above overflowed we compensate by
 		   incrementing.  This preserves the value modulo
@@ -1991,11 +1983,10 @@
 		if (x < v->ob_digit[i])
 			x++;
 	}
-#undef LONG_BIT_PyLong_SHIFT
 	x = x * sign;
-	if (x == -1)
-		x = -2;
-	return x;
+	if (x == (unsigned long)-1)
+		x = (unsigned long)-2;
+	return (long)x;
 }
 
 
@@ -3337,7 +3328,7 @@
 		/* Since PyLong_FromString doesn't have a length parameter,
 		 * check here for possible NULs in the string. */
 		char *string = PyString_AS_STRING(x);
-		if (strlen(string) != PyString_Size(x)) {
+		if (strlen(string) != (size_t)PyString_Size(x)) {
 			/* create a repr() of the input string,
 			 * just like PyLong_FromString does. */
 			PyObject *srepr;
@@ -3443,9 +3434,7 @@
 {
 	Py_ssize_t res;
 
-	res = v->ob_type->tp_basicsize;
-        if (v->ob_size != 0)
-		res += abs(v->ob_size) * sizeof(digit);
+	res = v->ob_type->tp_basicsize + ABS(Py_SIZE(v))*sizeof(digit);
 	return PyInt_FromSsize_t(res);
 }
 
@@ -3619,7 +3608,7 @@
 	PyObject_HEAD_INIT(&PyType_Type)
 	0,					/* ob_size */
 	"long",					/* tp_name */
-	sizeof(PyLongObject) - sizeof(digit),	/* tp_basicsize */
+	offsetof(PyLongObject, ob_digit),	/* tp_basicsize */
 	sizeof(digit),				/* tp_itemsize */
 	long_dealloc,				/* tp_dealloc */
 	0,					/* tp_print */