Index: Objects/intobject.c
===================================================================
--- Objects/intobject.c	(revision 63206)
+++ Objects/intobject.c	(working copy)
@@ -952,18 +952,31 @@
 static PyObject *
 int_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
 {
-	PyObject *x = NULL;
-	int base = -909;
+	PyObject *x = NULL, *baseo = NULL;
+	long base;
 	static char *kwlist[] = {"x", "base", 0};
 
 	if (type != &PyInt_Type)
 		return int_subtype_new(type, args, kwds); /* Wimp out */
-	if (!PyArg_ParseTupleAndKeywords(args, kwds, "|Oi:int", kwlist,
-					 &x, &base))
+	if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO:int", kwlist,
+					 &x, &baseo))
 		return NULL;
+	if (baseo) {
+		if (PyInt_Check(baseo))
+			base = PyInt_AS_LONG(baseo);
+		else if (PyLong_Check(baseo)) {
+			base = PyLong_AsLong(baseo);
+			if (base == -1 && PyErr_Occurred())
+				return NULL;
+		}
+		else {
+			PyErr_SetString(PyExc_TypeError, "an integer is required");
+			return NULL;
+		}
+	}
 	if (x == NULL)
 		return PyInt_FromLong(0L);
-	if (base == -909)
+	if (baseo == NULL)
 		return PyNumber_Int(x);
 	if (PyString_Check(x)) {
 		/* Since PyInt_FromString doesn't have a length parameter,
Index: Objects/longobject.c
===================================================================
--- Objects/longobject.c	(revision 63206)
+++ Objects/longobject.c	(working copy)
@@ -3319,18 +3319,31 @@
 static PyObject *
 long_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
 {
-	PyObject *x = NULL;
-	int base = -909;		     /* unlikely! */
+	PyObject *x = NULL, *baseo = NULL;
+	long base;
 	static char *kwlist[] = {"x", "base", 0};
 
 	if (type != &PyLong_Type)
 		return long_subtype_new(type, args, kwds); /* Wimp out */
-	if (!PyArg_ParseTupleAndKeywords(args, kwds, "|Oi:long", kwlist,
-					 &x, &base))
+	if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO:long", kwlist,
+					 &x, &baseo))
 		return NULL;
+	if (baseo) {
+		if (PyInt_Check(baseo))
+			base = PyInt_AS_LONG(baseo);
+		else if (PyLong_Check(baseo)) {
+			base = PyLong_AsLong(baseo);
+			if (base == -1 && PyErr_Occurred())
+				return NULL;
+		}
+		else {
+			PyErr_SetString(PyExc_TypeError, "an integer is required");
+			return NULL;
+		}
+	}
 	if (x == NULL)
 		return PyLong_FromLong(0L);
-	if (base == -909)
+	if (baseo == NULL)
 		return PyNumber_Long(x);
 	else if (PyString_Check(x)) {
 		/* Since PyLong_FromString doesn't have a length parameter,
Index: Lib/test/test_long.py
===================================================================
--- Lib/test/test_long.py	(revision 63206)
+++ Lib/test/test_long.py	(working copy)
@@ -398,7 +398,11 @@
         self.assertEqual(long('2br45qc', 35), 4294967297)
         self.assertEqual(long('1z141z5', 36), 4294967297)
 
+        # issue2844
+        self.assertRaises(ValueError, long, '42', -909)
+        self.assertRaises(TypeError, long, 42, 10)
 
+
     def test_conversion(self):
         # Test __long__()
         class ClassicMissingMethods: