diff --git a/Objects/longobject.c b/Objects/longobject.c
index 4e2cc41..c48502c 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -2211,16 +2211,17 @@ long_compare(PyLongObject *a, PyLongObject *b)
 	}
 	else {
 		Py_ssize_t i = PyLong_NDIGITS(a);
-		while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i])
-			;
-		if (i < 0)
-			sign = 0;
-		else {
-			sign = (int)a->ob_digit[i] - (int)b->ob_digit[i];
-			if (Py_SIZE(a) < 0)
+		if (i == 0)
+			return 0;
+		do {
+			--i;
+			sign = (sdigit)a->ob_digit[i] - b->ob_digit[i];
+			if (sign != 0)
+				break;
+		} while (i != 0);
+		if (PyLong_SIGN(a) < 0)
 				sign = -sign;
 		}
-	}
 	return sign < 0 ? -1 : sign > 0 ? 1 : 0;
 }
 
@@ -3256,6 +3257,21 @@ long_rshift(PyLongObject *a, PyLongObject *b)
 
 	CHECK_BINOP(a, b);
 
+	if (PyLong_FITS_INT(a) && PyLong_FITS_INT(b)) {
+		sdigit aa = PyLong_GET_INT(a);
+		sdigit bb = PyLong_GET_INT(b);
+		if (bb < 0) {
+			PyErr_SetString(PyExc_ValueError,
+					"negative shift count");
+			goto rshift_error;
+		}
+		if (bb < sizeof(aa)*8)
+			aa >>= bb;
+		else
+			aa = 0;
+		return PyLong_FromLong(aa);
+	}
+
 	if (Py_SIZE(a) < 0) {
 		/* Right shifting negative numbers is harder */
 		PyLongObject *a1, *a2;
@@ -3330,6 +3346,15 @@ long_lshift(PyObject *v, PyObject *w)
 				"outrageous left shift count");
 		goto lshift_error;
 	}
+
+	if ((shiftby < (sdigit)8 * sizeof(sdigit)) && PyLong_FITS_INT(a)) {
+		sdigit aa = PyLong_GET_INT(a);
+		sdigit bb = (sdigit)shiftby;
+		sdigit cc = aa << bb;
+		if ((cc >> bb) == aa)
+			return PyLong_FromLong(cc);
+	}
+
 	/* wordshift, remshift = divmod(shiftby, PyLong_SHIFT) */
 	wordshift = (int)shiftby / PyLong_SHIFT;
 	remshift  = (int)shiftby - wordshift * PyLong_SHIFT;