diff --git a/Include/graminit.h b/Include/graminit.h
diff --git a/Include/longintrepr.h b/Include/longintrepr.h
diff --git a/Objects/longobject.c b/Objects/longobject.c
index ecc71bb..fd00bbd 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -164,6 +164,7 @@ _PyLong_Copy(PyLongObject *src)
 	result = _PyLong_New(i);
 	if (result != NULL) {
 		Py_SIZE(result) = Py_SIZE(src);
+		/* FIXME: use memcpy() */
 		while (--i >= 0)
 			result->ob_digit[i] = src->ob_digit[i];
 	}
@@ -228,6 +229,11 @@ PyLong_FromLong(long ival)
 		digit *p = v->ob_digit;
 		Py_SIZE(v) = ndigits*sign;
 		t = abs_ival;
+		/* unroll the loop: we have at least two digits */
+		*p++ = (digit)(t & PyLong_MASK);
+		t >>= PyLong_SHIFT;
+		*p++ = (digit)(t & PyLong_MASK);
+		t >>= PyLong_SHIFT;
 		while (t) {
 			*p++ = (digit)(t & PyLong_MASK);
 			t >>= PyLong_SHIFT;
@@ -2852,6 +2858,13 @@ long_mul(PyLongObject *a, PyLongObject *b)
 		int sign;
 		PyLongObject *v;
 		sign = Py_SIZE(a) * Py_SIZE(b);
+		if (!(a->ob_digit[0] >> 15) && !(b->ob_digit[0] >> 15)) {
+			sdigit product = a->ob_digit[0];
+			product *= b->ob_digit[0];
+			if (sign < 0)
+				product = -product;
+			return PyLong_FromLong(product);
+		}
 		if (sign == 0)
 			return PyLong_FromLong(0L);
 		absv = (twodigits)a->ob_digit[0] * b->ob_digit[0];
@@ -2953,6 +2966,17 @@ long_div(PyObject *a, PyObject *b)
 	PyLongObject *div;

 	CHECK_BINOP(a, b);
+
+	/* fast path for single-digit divison */
+	if (ABS(Py_SIZE(a)) <= 1 && ABS(Py_SIZE(b)) <= 1) {
+		sdigit aa = MEDIUM_VALUE((PyLongObject*)a);
+		sdigit bb = MEDIUM_VALUE((PyLongObject*)b);
+		sdigit q = aa / bb;
+		if (((aa < 0) != (bb < 0)) && (aa % bb != 0))
+			q -= 1;
+		return PyLong_FromLong(q);
+	}
+
 	if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, NULL) < 0)
 		div = NULL;
 	return (PyObject *)div;
@@ -3008,6 +3032,16 @@ long_mod(PyObject *a, PyObject *b)

 	CHECK_BINOP(a, b);

+	/* fast path for single-digit modulo */
+	if (ABS(Py_SIZE(a)) <= 1 && ABS(Py_SIZE(b)) <= 1) {
+		sdigit aa = MEDIUM_VALUE((PyLongObject*)a);
+		sdigit bb = MEDIUM_VALUE((PyLongObject*)b);
+		sdigit r = aa % bb;
+		if (r && (aa < 0) != (bb < 0))
+			r += bb;
+		return PyLong_FromLong(r);
+	}
+
 	if (l_divmod((PyLongObject*)a, (PyLongObject*)b, NULL, &mod) < 0)
 		mod = NULL;
 	return (PyObject *)mod;
@@ -3228,7 +3262,7 @@ long_invert(PyLongObject *v)
 	PyLongObject *x;
 	PyLongObject *w;
 	if (ABS(Py_SIZE(v)) <=1)
-		return PyLong_FromLong(-(MEDIUM_VALUE(v)+1));
+		return PyLong_FromLong(~MEDIUM_VALUE(v));
 	w = (PyLongObject *)PyLong_FromLong(1L);
 	if (w == NULL)
 		return NULL;
@@ -3339,6 +3373,8 @@ long_lshift(PyObject *v, PyObject *w)

 	CHECK_BINOP(a, b);

+	/* FIXME: hacks small ints */
+
 	shiftby = PyLong_AsLong((PyObject *)b);
 	if (shiftby == -1L && PyErr_Occurred())
 		goto lshift_error;
@@ -3397,6 +3433,18 @@ long_bitwise(PyLongObject *a,
 	digit diga, digb;
 	PyObject *v;

+	if (ABS(Py_SIZE(a)) <= 1 && ABS(Py_SIZE(b)) <= 1) {
+		sdigit aa = MEDIUM_VALUE((PyLongObject*)a);
+		sdigit bb = MEDIUM_VALUE((PyLongObject*)b);
+		sdigit r;
+		switch (op) {
+		case '^': r = aa ^ bb; break;
+		case '&': r = aa & bb; break;
+		case '|': r = aa | bb; break;
+		}
+		return PyLong_FromLong(r);
+	}
+
 	if (Py_SIZE(a) < 0) {
 		a = (PyLongObject *) long_invert(a);
 		if (a == NULL)
diff --git a/Python/graminit.c b/Python/graminit.c