diff --git a/Lib/test/test_builtin.py b/Lib/test/test_builtin.py
index 6671f2c02eb..19ce9ec83d3 100644
--- a/Lib/test/test_builtin.py
+++ b/Lib/test/test_builtin.py
@@ -1224,6 +1224,9 @@ class BuiltinTest(unittest.TestCase):
         self.assertEqual(round(-5.5), -6)
         self.assertEqual(round(-6.5), -7)
 
+        # Issue #1869: integral floats should remain unchanged
+        self.assertEqual(round(5e15+1), 5e15+1)
+
         # Check behavior on ints
         self.assertEqual(round(0), 0)
         self.assertEqual(round(8), 8)
diff --git a/Misc/NEWS b/Misc/NEWS
index f226eb1a39e..58197de0490 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,9 @@ What's New in Python 2.7 alpha 1
 Core and Builtins
 -----------------
 
+- Issue #1869: fix a couple of minor round() issues.  round(5e15+1)
+    was giving 5e15+2; round(-0.0) was losing the sign of the zero.
+
 - Issue #5759: float() didn't call __float__ on str subclasses.
 
 - Issue #5704: the "-3" command-line option now implies "-t".
diff --git a/Python/bltinmodule.c b/Python/bltinmodule.c
index 0f3392a56f8..8f6e85555a8 100644
--- a/Python/bltinmodule.c
+++ b/Python/bltinmodule.c
@@ -2081,10 +2081,7 @@ builtin_round(PyObject *self, PyObject *args, PyObject *kwds)
 		number /= f;
 	else
 		number *= f;
-	if (number >= 0.0)
-		number = floor(number + 0.5);
-	else
-		number = ceil(number - 0.5);
+	number = round(number);
 	if (ndigits < 0)
 		number *= f;
 	else