diff --git a/Lib/test/test_complex.py b/Lib/test/test_complex.py
index f27593e..69e2715 100644
--- a/Lib/test/test_complex.py
+++ b/Lib/test/test_complex.py
@@ -129,7 +129,7 @@
         self.assertTrue(a < 2.0j)
 
     def test_richcompare(self):
-        self.assertRaises(OverflowError, complex.__eq__, 1+1j, 1L<<10000)
+        self.assertEqual(complex.__eq__(1+1j, 1L<<10000), False)
         self.assertEqual(complex.__lt__(1+1j, None), NotImplemented)
         self.assertIs(complex.__eq__(1+1j, 1+1j), True)
         self.assertIs(complex.__eq__(1+1j, 2+2j), False)
@@ -140,6 +140,23 @@
         self.assertRaises(TypeError, complex.__gt__, 1+1j, 2+2j)
         self.assertRaises(TypeError, complex.__ge__, 1+1j, 2+2j)
 
+    def test_richcompare_boundaries(self):
+        def check(n, deltas, is_equal, imag = 0.0):
+            for delta in deltas:
+                i = n + delta
+                z = complex(i, imag)
+                self.assertIs(complex.__eq__(z, i), is_equal(delta))
+                self.assertIs(complex.__ne__(z, i), not is_equal(delta))
+        # For IEEE-754 doubles the following should hold:
+        #    x in [2 ** (52 + i), 2 ** (53 + i + 1)] -> x mod 2 ** i == 0
+        # where the interval is representable, of course.
+        for i in range(1, 10):
+            pow = 52 + i
+            mult = 2 ** i
+            check(2 ** pow, range(1, 101), lambda delta: delta % mult == 0)
+            check(2 ** pow, range(1, 101), lambda delta: False, float(i))
+        check(2 ** 53, range(-100, 0), lambda delta: True)
+
     def test_mod(self):
         self.assertRaises(ZeroDivisionError, (1+1j).__mod__, 0+0j)
 
diff --git a/Misc/NEWS b/Misc/NEWS
index e63d905..352ebf4 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,13 @@
 Core and Builtins
 -----------------
 
+- Issue #8748: Fix two issues with comparisons between complex and integer
+  objects.  (1) The comparison could incorrectly return True in some cases
+  (2**53+1 == complex(2**53) == 2**53), breaking transivity of equality.
+  (2) The comparison raised an OverflowError for large integers, leading
+  to unpredictable exceptions when combining integers and complex objects
+  in sets or dicts.
+
 - Issue #5211: Implicit coercion for the complex type is now completely
   removed.  (Coercion for arithmetic operations was already removed in 2.7
   alpha 4, but coercion for rich comparisons was accidentally left in.)
diff --git a/Objects/complexobject.c b/Objects/complexobject.c
index dacafe6..677ac0e 100644
--- a/Objects/complexobject.c
+++ b/Objects/complexobject.c
@@ -783,25 +783,70 @@
 static PyObject *
 complex_richcompare(PyObject *v, PyObject *w, int op)
 {
-    Py_complex i, j;
     PyObject *res;
-
-    TO_COMPLEX(v, i);
-    TO_COMPLEX(w, j);
+    Py_complex i;
+    int equal;
 
     if (op != Py_EQ && op != Py_NE) {
-        PyErr_SetString(PyExc_TypeError,
-            "no ordering relation is defined for complex numbers");
-        return NULL;
+        /* for backwards compatibility, comparisons with non-numbers return
+         * NotImplemented.  Only comparisons with core numeric types raise
+         * TypeError.
+         */
+        if (PyInt_Check(w) || PyLong_Check(w) ||
+            PyFloat_Check(w) || PyComplex_Check(w)) {
+            PyErr_SetString(PyExc_TypeError,
+                            "no ordering relation is defined "
+                            "for complex numbers");
+            return NULL;
+        }
+        goto Unimplemented;
     }
 
-    if ((i.real == j.real && i.imag == j.imag) == (op == Py_EQ))
-        res = Py_True;
+    assert(PyComplex_Check(v));
+    TO_COMPLEX(v, i);
+
+    if (PyInt_Check(w) || PyLong_Check(w)) {
+        /* Check for 0.0 imaginary part first to avoid the rich
+         * comparison when possible.
+         */
+        if (i.imag == 0.0) {
+            PyObject *j, *sub_res;
+            j = PyFloat_FromDouble(i.real);
+            if (j == NULL)
+                return NULL;
+
+            sub_res = PyObject_RichCompare(j, w, op);
+            Py_DECREF(j);
+            return sub_res;
+        }
+        else {
+            equal = 0;
+        }
+    }
+    else if (PyFloat_Check(w)) {
+        equal = (i.real == PyFloat_AsDouble(w) && i.imag == 0.0);
+    }
+    else if (PyComplex_Check(w)) {
+        Py_complex j;
+
+        TO_COMPLEX(w, j);
+        equal = (i.real == j.real && i.imag == j.imag);
+    }
+    else {
+        goto Unimplemented;
+    }
+
+    if (equal == (op == Py_EQ))
+         res = Py_True;
     else
-        res = Py_False;
+         res = Py_False;
 
     Py_INCREF(res);
     return res;
+
+  Unimplemented:
+    Py_INCREF(Py_NotImplemented);
+    return Py_NotImplemented;
 }
 
 static PyObject *