diff --git a/changelog.d/5174.bugfix b/changelog.d/5174.bugfix
new file mode 100644
index 0000000000..0f26d46b2c
--- /dev/null
+++ b/changelog.d/5174.bugfix
@@ -0,0 +1 @@
+Re-order stages in registration flows such that msisdn and email verification are done last.
diff --git a/synapse/rest/client/v2_alpha/register.py b/synapse/rest/client/v2_alpha/register.py
index fa0cedb8d4..042f636135 100644
--- a/synapse/rest/client/v2_alpha/register.py
+++ b/synapse/rest/client/v2_alpha/register.py
@@ -348,18 +348,22 @@ class RegisterRestServlet(RestServlet):
         if self.hs.config.enable_registration_captcha:
             # only support 3PIDless registration if no 3PIDs are required
             if not require_email and not require_msisdn:
-                flows.extend([[LoginType.RECAPTCHA]])
+                # Also add a dummy flow here, otherwise if a client completes
+                # recaptcha first we'll assume they were going for this flow
+                # and complete the request, when they could have been trying to
+                # complete one of the flows with email/msisdn auth.
+                flows.extend([[LoginType.RECAPTCHA, LoginType.DUMMY]])
             # only support the email-only flow if we don't require MSISDN 3PIDs
             if not require_msisdn:
-                flows.extend([[LoginType.EMAIL_IDENTITY, LoginType.RECAPTCHA]])
+                flows.extend([[LoginType.RECAPTCHA, LoginType.EMAIL_IDENTITY]])
 
             if show_msisdn:
                 # only support the MSISDN-only flow if we don't require email 3PIDs
                 if not require_email:
-                    flows.extend([[LoginType.MSISDN, LoginType.RECAPTCHA]])
+                    flows.extend([[LoginType.RECAPTCHA, LoginType.MSISDN]])
                 # always let users provide both MSISDN & email
                 flows.extend([
-                    [LoginType.MSISDN, LoginType.EMAIL_IDENTITY, LoginType.RECAPTCHA],
+                    [LoginType.RECAPTCHA, LoginType.MSISDN, LoginType.EMAIL_IDENTITY],
                 ])
         else:
             # only support 3PIDless registration if no 3PIDs are required
@@ -382,7 +386,15 @@ class RegisterRestServlet(RestServlet):
         if self.hs.config.user_consent_at_registration:
             new_flows = []
             for flow in flows:
-                flow.append(LoginType.TERMS)
+                inserted = False
+                # m.login.terms should go near the end but before msisdn or email auth
+                for i, stage in enumerate(flow):
+                    if stage == LoginType.EMAIL_IDENTITY or stage == LoginType.MSISDN:
+                        flow.insert(i, LoginType.TERMS)
+                        inserted = True
+                        break
+                if not inserted:
+                    flow.append(LoginType.TERMS)
             flows.extend(new_flows)
 
         auth_result, params, session_id = yield self.auth_handler.check_auth(
diff --git a/tests/rest/client/v2_alpha/test_auth.py b/tests/rest/client/v2_alpha/test_auth.py
index ad7d476401..b9ef46e8fb 100644
--- a/tests/rest/client/v2_alpha/test_auth.py
+++ b/tests/rest/client/v2_alpha/test_auth.py
@@ -92,7 +92,14 @@ class FallbackAuthTests(unittest.HomeserverTestCase):
         self.assertEqual(len(self.recaptcha_attempts), 1)
         self.assertEqual(self.recaptcha_attempts[0][0]["response"], "a")
 
-        # Now we have fufilled the recaptcha fallback step, we can then send a
+        # also complete the dummy auth
+        request, channel = self.make_request(
+            "POST", "register", {"auth": {"session": session, "type": "m.login.dummy"}}
+        )
+        self.render(request)
+
+        # Now we should have fufilled a complete auth flow, including
+        # the recaptcha fallback step, we can then send a
         # request to the register API with the session in the authdict.
         request, channel = self.make_request(
             "POST", "register", {"auth": {"session": session}}
diff --git a/tests/test_terms_auth.py b/tests/test_terms_auth.py
index f412985d2c..52739fbabc 100644
--- a/tests/test_terms_auth.py
+++ b/tests/test_terms_auth.py
@@ -59,7 +59,7 @@ class TermsTestCase(unittest.HomeserverTestCase):
         for flow in channel.json_body["flows"]:
             self.assertIsInstance(flow["stages"], list)
             self.assertTrue(len(flow["stages"]) > 0)
-            self.assertEquals(flow["stages"][-1], "m.login.terms")
+            self.assertTrue("m.login.terms" in flow["stages"])
 
         expected_params = {
             "m.login.terms": {