diff --git a/OpenSSL/crypto/x509.c b/OpenSSL/crypto/x509.c
index 2f12437..915a3b7 100644
--- a/OpenSSL/crypto/x509.c
+++ b/OpenSSL/crypto/x509.c
@@ -776,8 +776,7 @@
 }
 
 PyTypeObject crypto_X509_Type = {
-    PyObject_HEAD_INIT(NULL)
-    0,
+    PyVarObject_HEAD_INIT(&PyType_Type, 0)
     "X509",
     sizeof(crypto_X509Obj),
     0,
diff --git a/OpenSSL/crypto/x509name.c b/OpenSSL/crypto/x509name.c
index 39fdcf8..c288180 100644
--- a/OpenSSL/crypto/x509name.c
+++ b/OpenSSL/crypto/x509name.c
@@ -162,7 +162,7 @@
          * See lp#314814.
          */
         flush_error_queue();
-        return Py_FindMethod(crypto_X509Name_methods, (PyObject *)self, name);
+        return crypto_X509Name_Type.tp_getattr((PyObject*)self, name);
     }
 
     len = get_name_by_nid(self->x509_name, nid, &utf8string);
@@ -216,16 +216,50 @@
  *            m - The second X509Name
  * Returns:   <0 if n < m, 0 if n == m and >0 if n > m
  */
-static int
-crypto_X509Name_compare(crypto_X509NameObj *n, crypto_X509NameObj *m)
-{
-    int result = X509_NAME_cmp(n->x509_name, m->x509_name);
-    if (result < 0) {
-        return -1;
-    } else if (result > 0) {
-        return 1;
+static PyObject *
+crypto_X509Name_richcompare(PyObject *n, PyObject *m, int op) {
+    int result;
+
+    if (!crypto_X509Name_Check(n) || !crypto_X509Name_Check(m)) {
+        Py_INCREF(Py_NotImplemented);
+        return Py_NotImplemented;
+    }
+
+    result = X509_NAME_cmp(
+        ((crypto_X509NameObj*)n)->x509_name,
+        ((crypto_X509NameObj*)m)->x509_name);
+
+    switch (op) {
+    case Py_EQ:
+        result = (result == 0);
+
+    case Py_NE:
+        result = (result != 0);
+
+    case Py_LT:
+        result = (result < 0);
+
+    case Py_LE:
+        result = (result <= 0);
+
+    case Py_GT:
+        result = (result > 0);
+
+    case Py_GE:
+        result = (result >= 0);
+
+    default:
+        /* Should be impossible */
+        Py_INCREF(Py_NotImplemented);
+        return Py_NotImplemented;
+    }
+
+    if (result) {
+        Py_INCREF(Py_True);
+        return Py_True;
     } else {
-        return 0;
+        Py_INCREF(Py_False);
+        return Py_False;
     }
 }
 
@@ -250,7 +284,7 @@
     {
         /* This is safe because tmpbuf is max 512 characters */
         sprintf(realbuf, "<X509Name object '%s'>", tmpbuf);
-        return PyString_FromString(realbuf);
+        return PyText_FromString(realbuf);
     }
 }
 
@@ -275,7 +309,7 @@
         return NULL;
     }
     hash = X509_NAME_hash(self->x509_name);
-    return PyInt_FromLong(hash);
+    return PyLong_FromLong(hash);
 }
 
 static char crypto_X509Name_der_doc[] = "\n\
@@ -296,8 +330,8 @@
     }
 
     i2d_X509_NAME(self->x509_name, 0);
-    return PyString_FromStringAndSize(self->x509_name->bytes->data,
-				      self->x509_name->bytes->length);
+    return PyBytes_FromStringAndSize(self->x509_name->bytes->data,
+                                     self->x509_name->bytes->length);
 }
 
 
@@ -342,8 +376,8 @@
 	/* printf("fname is %s len=%d str=%s\n", OBJ_nid2sn(nid), l, str); */
 
 	tuple = PyTuple_New(2);
-	PyTuple_SetItem(tuple, 0, PyString_FromString(OBJ_nid2sn(nid)));
-	PyTuple_SetItem(tuple, 1, PyString_FromStringAndSize((char *)str, l));
+	PyTuple_SetItem(tuple, 0, PyBytes_FromString(OBJ_nid2sn(nid)));
+	PyTuple_SetItem(tuple, 1, PyBytes_FromStringAndSize((char *)str, l));
 
 	PyList_SetItem(list, i, tuple);
     }
@@ -421,8 +455,7 @@
 #undef ADD_METHOD
 
 PyTypeObject crypto_X509Name_Type = {
-    PyObject_HEAD_INIT(NULL)
-    0,
+    PyVarObject_HEAD_INIT(&PyType_Type, 0)
     "X509Name",
     sizeof(crypto_X509NameObj),
     0,
@@ -430,7 +463,7 @@
     NULL, /* print */
     (getattrfunc)crypto_X509Name_getattr,
     (setattrfunc)crypto_X509Name_setattr,
-    (cmpfunc)crypto_X509Name_compare,
+    NULL, /* reserved */
     (reprfunc)crypto_X509Name_repr,
     NULL, /* as_number */
     NULL, /* as_sequence */
@@ -445,7 +478,7 @@
     crypto_X509Name_doc, /* tp_doc */
     (traverseproc)crypto_X509Name_traverse, /* tp_traverse */
     (inquiry)crypto_X509Name_clear, /* tp_clear */
-    NULL, /* tp_richcompare */
+    crypto_X509Name_richcompare, /* tp_richcompare */
     0, /* tp_weaklistoffset */
     NULL, /* tp_iter */
     NULL, /* tp_iternext */
diff --git a/OpenSSL/py3k.h b/OpenSSL/py3k.h
index 55bcfda..dc46b43 100644
--- a/OpenSSL/py3k.h
+++ b/OpenSSL/py3k.h
@@ -13,6 +13,8 @@
 
 #else /* (PY_VERSION_HEX >= 0x03000000) */
 
+#define PyVarObject_HEAD_INIT(type, size) PyObject_HEAD_INIT(NULL) 0
+
 #define PyBytes_FromStringAndSize PyString_FromStringAndSize
 
 #define PyLong_FromLong PyInt_FromLong