diff --git a/Lib/test/test_codecs.py b/Lib/test/test_codecs.py
index 4ec7b5865cc..e060471d4b0 100644
--- a/Lib/test/test_codecs.py
+++ b/Lib/test/test_codecs.py
@@ -1549,6 +1549,11 @@ def test_charmap(self):
         self.assertEqual("foo\udca5bar".encode("iso-8859-3", "surrogateescape"),
                          b"foo\xa5bar")
 
+    def test_latin1(self):
+        # Issue6373
+        self.assertEqual("\udce4\udceb\udcef\udcf6\udcfc".encode("latin1", "surrogateescape"),
+                         b"\xe4\xeb\xef\xf6\xfc")
+
 
 def test_main():
     support.run_unittest(
diff --git a/Misc/NEWS b/Misc/NEWS
index 2381844249c..98539e53173 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,10 @@ What's New in Python 3.2 Alpha 1?
 Core and Builtins
 -----------------
 
+- Issue #6373: Fixed a RuntimeError when encoding with the latin-1 codec and
+  the 'surrogateescape' error handler, a string which contains unpaired
+  surrogates.
+
 - Issue #4856: Remove checks for win NT.
 
 Library
diff --git a/Objects/unicodeobject.c b/Objects/unicodeobject.c
index 0d4a3ddd806..305289bc78c 100644
--- a/Objects/unicodeobject.c
+++ b/Objects/unicodeobject.c
@@ -4201,10 +4201,12 @@ static PyObject *unicode_encode_ucs1(const Py_UNICODE *p,
                     repsize = PyBytes_Size(repunicode);
                     if (repsize > 1) {
                         /* Make room for all additional bytes. */
+                        respos = str - PyBytes_AS_STRING(res);
                         if (_PyBytes_Resize(&res, ressize+repsize-1)) {
                             Py_DECREF(repunicode);
                             goto onError;
                         }
+                        str = PyBytes_AS_STRING(res) + respos;
                         ressize += repsize-1;
                     }
                     memcpy(str, PyBytes_AsString(repunicode), repsize);