diff --git a/Lib/test/test_mmap.py b/Lib/test/test_mmap.py
index 605ad3d..efd1b1e 100644
--- a/Lib/test/test_mmap.py
+++ b/Lib/test/test_mmap.py
@@ -21,12 +21,12 @@
         # Test mmap module on Unix systems and Windows
 
         # Create a file to be mmap'ed.
-        f = open(TESTFN, 'w+')
+        f = open(TESTFN, 'bw+')
         try:
             # Write 2 pages worth of data to the file
-            f.write('\0'* PAGESIZE)
-            f.write('foo')
-            f.write('\0'* (PAGESIZE-3) )
+            f.write(b'\0'* PAGESIZE)
+            f.write(b'foo')
+            f.write(b'\0'* (PAGESIZE-3) )
             f.flush()
             m = mmap.mmap(f.fileno(), 2 * PAGESIZE)
             f.close()
@@ -38,17 +38,17 @@
 
             self.assertEqual(len(m), 2*PAGESIZE)
 
-            self.assertEqual(m[0], '\0')
-            self.assertEqual(m[0:3], '\0\0\0')
+            self.assertEqual(m[0], b'\0')
+            self.assertEqual(m[0:3], b'\0\0\0')
 
             # Modify the file's content
-            m[0] = '3'
-            m[PAGESIZE +3: PAGESIZE +3+3] = 'bar'
+            m[0] = b'3'
+            m[PAGESIZE +3: PAGESIZE +3+3] = b'bar'
 
             # Check that the modification worked
-            self.assertEqual(m[0], '3')
-            self.assertEqual(m[0:3], '3\0\0')
-            self.assertEqual(m[PAGESIZE-1 : PAGESIZE + 7], '\0foobar\0')
+            self.assertEqual(m[0], b'3')
+            self.assertEqual(m[0:3], b'3\0\0')
+            self.assertEqual(m[PAGESIZE-1 : PAGESIZE + 7], b'\0foobar\0')
 
             m.flush()
 
@@ -113,14 +113,14 @@
     def test_access_parameter(self):
         # Test for "access" keyword parameter
         mapsize = 10
-        open(TESTFN, "wb").write("a"*mapsize)
+        open(TESTFN, "wb").write(b"a"*mapsize)
         f = open(TESTFN, "rb")
         m = mmap.mmap(f.fileno(), mapsize, access=mmap.ACCESS_READ)
-        self.assertEqual(m[:], 'a'*mapsize, "Readonly memory map data incorrect.")
+        self.assertEqual(m[:], b'a'*mapsize, "Readonly memory map data incorrect.")
 
         # Ensuring that readonly mmap can't be slice assigned
         try:
-            m[:] = 'b'*mapsize
+            m[:] = b'b'*mapsize
         except TypeError:
             pass
         else:
@@ -128,7 +128,7 @@
 
         # Ensuring that readonly mmap can't be item assigned
         try:
-            m[0] = 'b'
+            m[0] = b'b'
         except TypeError:
             pass
         else:
@@ -137,7 +137,7 @@
         # Ensuring that readonly mmap can't be write() to
         try:
             m.seek(0,0)
-            m.write('abc')
+            m.write(b'abc')
         except TypeError:
             pass
         else:
@@ -146,7 +146,7 @@
         # Ensuring that readonly mmap can't be write_byte() to
         try:
             m.seek(0,0)
-            m.write_byte('d')
+            m.write_byte(b'd')
         except TypeError:
             pass
         else:
@@ -162,7 +162,7 @@
         else:
             self.fail("Able to resize readonly memory map")
         del m, f
-        self.assertEqual(open(TESTFN, "rb").read(), 'a'*mapsize,
+        self.assertEqual(open(TESTFN, "rb").read(), b'a'*mapsize,
                "Readonly memory map data file was modified")
 
         # Opening mmap with size too big
@@ -193,8 +193,8 @@
         f = open(TESTFN, "r+b")
         m = mmap.mmap(f.fileno(), mapsize, access=mmap.ACCESS_WRITE)
         # Modifying write-through memory map
-        m[:] = 'c'*mapsize
-        self.assertEqual(m[:], 'c'*mapsize,
+        m[:] = b'c'*mapsize
+        self.assertEqual(m[:], b'c'*mapsize,
                "Write-through memory map memory not updated properly.")
         m.flush()
         m.close()
@@ -202,18 +202,18 @@
         f = open(TESTFN, 'rb')
         stuff = f.read()
         f.close()
-        self.assertEqual(stuff, 'c'*mapsize,
+        self.assertEqual(stuff, b'c'*mapsize,
                "Write-through memory map data file not updated properly.")
 
         # Opening mmap with access=ACCESS_COPY
         f = open(TESTFN, "r+b")
         m = mmap.mmap(f.fileno(), mapsize, access=mmap.ACCESS_COPY)
         # Modifying copy-on-write memory map
-        m[:] = 'd'*mapsize
-        self.assertEqual(m[:], 'd' * mapsize,
+        m[:] = b'd'*mapsize
+        self.assertEqual(m[:], b'd' * mapsize,
                "Copy-on-write memory map data not written correctly.")
         m.flush()
-        self.assertEqual(open(TESTFN, "rb").read(), 'c'*mapsize,
+        self.assertEqual(open(TESTFN, "rb").read(), b'c'*mapsize,
                "Copy-on-write test data file should not be modified.")
         # Ensuring copy-on-write maps cannot be resized
         self.assertRaises(TypeError, m.resize, 2*mapsize)
@@ -239,9 +239,9 @@
     def test_tougher_find(self):
         # Do a tougher .find() test.  SF bug 515943 pointed out that, in 2.2,
         # searching for data with embedded \0 bytes didn't work.
-        f = open(TESTFN, 'w+')
+        f = open(TESTFN, 'wb+')
 
-        data = 'aabaac\x00deef\x00\x00aa\x00'
+        data = b'aabaac\x00deef\x00\x00aa\x00'
         n = len(data)
         f.write(data)
         f.flush()
@@ -252,14 +252,14 @@
             for finish in range(start, n+1):
                 slice = data[start : finish]
                 self.assertEqual(m.find(slice), data.find(slice))
-                self.assertEqual(m.find(slice + 'x'), -1)
+                self.assertEqual(m.find(slice + b'x'), -1)
         m.close()
 
     def test_double_close(self):
         # make sure a double close doesn't crash on Solaris (Bug# 665913)
-        f = open(TESTFN, 'w+')
+        f = open(TESTFN, 'wb+')
 
-        f.write(2**16 * 'a') # Arbitrary character
+        f.write(2**16 * b'a') # Arbitrary character
         f.close()
 
         f = open(TESTFN)
@@ -271,28 +271,28 @@
     def test_entire_file(self):
         # test mapping of entire file by passing 0 for map length
         if hasattr(os, "stat"):
-            f = open(TESTFN, "w+")
+            f = open(TESTFN, "wb+")
 
-            f.write(2**16 * 'm') # Arbitrary character
+            f.write(2**16 * b'm') # Arbitrary character
             f.close()
 
             f = open(TESTFN, "rb+")
             mf = mmap.mmap(f.fileno(), 0)
             self.assertEqual(len(mf), 2**16, "Map size should equal file size.")
-            self.assertEqual(mf.read(2**16), 2**16 * "m")
+            self.assertEqual(mf.read(2**16), 2**16 * b"m")
             mf.close()
             f.close()
 
     def test_move(self):
         # make move works everywhere (64-bit format problem earlier)
-        f = open(TESTFN, 'w+')
+        f = open(TESTFN, 'wb+')
 
-        f.write("ABCDEabcde") # Arbitrary character
+        f.write(b"ABCDEabcde") # Arbitrary character
         f.flush()
 
         mf = mmap.mmap(f.fileno(), 10)
         mf.move(5, 0, 5)
-        self.assertEqual(mf[:], "ABCDEABCDE", "Map move should have duplicated front 5")
+        self.assertEqual(mf[:], b"ABCDEABCDE", "Map move should have duplicated front 5")
         mf.close()
         f.close()
 
@@ -300,11 +300,13 @@
         # anonymous mmap.mmap(-1, PAGE)
         m = mmap.mmap(-1, PAGESIZE)
         for x in range(PAGESIZE):
-            self.assertEqual(m[x], '\0', "anonymously mmap'ed contents should be zero")
+            self.assertEqual(m[x], b'\0', "anonymously mmap'ed contents should be zero")
 
+        b = bytes(1)
         for x in range(PAGESIZE):
-            m[x] = ch = chr(x & 255)
-            self.assertEqual(m[x], ch)
+            b[0] = x & 255
+            m[x] = b
+            self.assertEqual(m[x], b)
 
 def test_main():
     run_unittest(MmapTests)
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;
 }