diff --git a/Lib/test/test_complex.py b/Lib/test/test_complex.py
index 6441208..f6c7cc3 100644
--- a/Lib/test/test_complex.py
+++ b/Lib/test/test_complex.py
@@ -110,12 +110,18 @@
         self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 0+0j)
 
     def test_richcompare(self):
-        self.assertRaises(OverflowError, complex.__eq__, 1+1j, 1<<10000)
+        self.assertIs(complex.__eq__(1+1j, 1<<10000), False)
         self.assertIs(complex.__lt__(1+1j, None), NotImplemented)
         self.assertIs(complex.__eq__(1+1j, 1+1j), True)
         self.assertIs(complex.__eq__(1+1j, 2+2j), False)
         self.assertIs(complex.__ne__(1+1j, 1+1j), False)
         self.assertIs(complex.__ne__(1+1j, 2+2j), True)
+        for i in range(1, 100):
+            f = i / 100.0
+            self.assertIs(complex.__eq__(f+0j, f), True)
+            self.assertIs(complex.__ne__(f+0j, f), False)
+            self.assertIs(complex.__eq__(complex(f, f), f), False)
+            self.assertIs(complex.__ne__(complex(f, f), f), True)
         self.assertIs(complex.__lt__(1+1j, 2+2j), NotImplemented)
         self.assertIs(complex.__le__(1+1j, 2+2j), NotImplemented)
         self.assertIs(complex.__gt__(1+1j, 2+2j), NotImplemented)
@@ -129,6 +135,23 @@
         self.assertIs(operator.ne(1+1j, 1+1j), False)
         self.assertIs(operator.ne(1+1j, 2+2j), True)
 
+    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):
         # % is no longer supported on complex numbers
         self.assertRaises(TypeError, (1+1j).__mod__, 0+0j)
diff --git a/Misc/NEWS b/Misc/NEWS
index 5ac16df..9772a15 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,19 @@
 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 #8748: Fix comparisons between complex and integer objects.
+  These used to convert the integer object to a complex number before
+  doing the comparison, giving a potentially incorrect result when
+  that conversion involved precision loss.  (Ex: 2**53+1 ==
+  complex(2**53) returned True; now returns False.)
+
 - Issue #8766: Initialize _warnings module before importing the first module.
   Fix a crash if an empty directory called "encodings" exists in sys.path.
 
diff --git a/Objects/complexobject.c b/Objects/complexobject.c
index ec26e0a..9e1e217 100644
--- a/Objects/complexobject.c
+++ b/Objects/complexobject.c
@@ -620,22 +620,58 @@
 complex_richcompare(PyObject *v, PyObject *w, int op)
 {
     PyObject *res;
-    Py_complex i, j;
-    TO_COMPLEX(v, i);
-    TO_COMPLEX(w, j);
+    Py_complex i;
+    int equal;
 
     if (op != Py_EQ && op != Py_NE) {
-        Py_INCREF(Py_NotImplemented);
-        return Py_NotImplemented;
+        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 (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 *