diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index d39169a..5afe715 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -206,7 +206,7 @@
 	else
 		++eol;		/* we're interested in the position after the
 				   newline. */
-	result = PyString_FromStringAndSize(start, (eol - start));
+	result = PyBytes_FromStringAndSize(start, (eol - start));
 	self->pos += (eol - start);
 	return result;
 }
@@ -659,7 +659,7 @@
 		PyErr_SetString(PyExc_IndexError, "mmap index out of range");
 		return NULL;
 	}
-	return PyString_FromStringAndSize(self->data + i, 1);
+	return PyBytes_FromStringAndSize(self->data + i, 1);
 }
 
 static PyObject *
@@ -677,7 +677,7 @@
 	else if ((size_t)ihigh > self->size)
 		ihigh = self->size;
 
-	return PyString_FromStringAndSize(self->data + ilow, ihigh-ilow);
+	return PyBytes_FromStringAndSize(self->data + ilow, ihigh-ilow);
 }
 
 static PyObject *
@@ -720,19 +720,19 @@
 				"mmap object doesn't support slice deletion");
 		return -1;
 	}
-	if (! (PyString_Check(v)) ) {
+	if (! (PyBytes_Check(v)) ) {
 		PyErr_SetString(PyExc_IndexError,
-				"mmap slice assignment must be a string");
+				"mmap slice assignment must be bytes");
 		return -1;
 	}
-	if (PyString_Size(v) != (ihigh - ilow)) {
+	if (PyBytes_Size(v) != (ihigh - ilow)) {
 		PyErr_SetString(PyExc_IndexError,
 				"mmap slice assignment is wrong size");
 		return -1;
 	}
 	if (!is_writeable(self))
 		return -1;
-	buf = PyString_AsString(v);
+	buf = PyBytes_AsString(v);
 	memcpy(self->data + ilow, buf, ihigh-ilow);
 	return 0;
 }
@@ -752,14 +752,14 @@
 				"mmap object doesn't support item deletion");
 		return -1;
 	}
-	if (! (PyString_Check(v) && PyString_Size(v)==1) ) {
+	if (! (PyBytes_Check(v) && PyBytes_Size(v)==1) ) {
 		PyErr_SetString(PyExc_IndexError,
 				"mmap assignment must be single-character string");
 		return -1;
 	}
 	if (!is_writeable(self))
 		return -1;
-	buf = PyString_AsString(v);
+	buf = PyBytes_AsString(v);
 	self->data[i] = buf[0];
 	return 0;
 }