diff --git a/version.py b/version.py
index 537946f336..32d797ef66 100644
--- a/version.py
+++ b/version.py
@@ -13,6 +13,13 @@ LATEST_MAJOR_VERSION = "2.1"
 LATEST_RELEASE_VERSION = "2.1.2"
 LATEST_RELEASE_ANNOUNCEMENT = "https://blog.zulip.org/2019/12/13/zulip-2-1-released/"
 
+# Versions of the desktop app below DESKTOP_MINIMUM_VERSION will be
+# prevented from connecting to the Zulip server.  Versions above
+# DESKTOP_MINIMUM_VERSION but below DESKTOP_WARNING_VERSION will have
+# a banner at the top of the page asking the user to upgrade.
+DESKTOP_MINIMUM_VERSION = "5.0.0"
+DESKTOP_WARNING_VERSION = "5.0.0"
+
 # Bump the minor PROVISION_VERSION to indicate that folks should provision
 # only when going from an old version of the code to a newer version. Bump
 # the major version to indicate that folks should provision in both
diff --git a/zerver/tests/test_compatibility.py b/zerver/tests/test_compatibility.py
index 494f825e01..458ccf40e1 100644
--- a/zerver/tests/test_compatibility.py
+++ b/zerver/tests/test_compatibility.py
@@ -1,3 +1,5 @@
+import mock
+
 from zerver.lib.test_classes import ZulipTestCase
 from zerver.views.compatibility import find_mobile_os, version_lt, is_outdated_desktop_app
 
@@ -96,8 +98,15 @@ class CompatibilityTest(ZulipTestCase):
     def test_insecure_desktop_app(self) -> None:
         self.assertEqual(is_outdated_desktop_app('ZulipDesktop/0.5.2 (Mac)'), (True, True, True))
         self.assertEqual(is_outdated_desktop_app('ZulipElectron/2.3.82 Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Zulip/2.3.82 Chrome/61.0.3163.100 Electron/2.0.9 Safari/537.36'), (True, True, True))
-        self.assertEqual(is_outdated_desktop_app('ZulipElectron/4.0.0 Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Zulip/4.0.3 Chrome/66.0.3359.181 Electron/3.1.10 Safari/537.36'), (True, False, False))
-        self.assertEqual(is_outdated_desktop_app('ZulipElectron/4.0.3 Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Zulip/4.0.3 Chrome/66.0.3359.181 Electron/3.1.10 Safari/537.36'), (False, False, False))
+        self.assertEqual(is_outdated_desktop_app('ZulipElectron/4.0.0 Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Zulip/4.0.3 Chrome/66.0.3359.181 Electron/3.1.10 Safari/537.36'), (True, True, False))
+
+        self.assertEqual(is_outdated_desktop_app('ZulipElectron/4.0.3 Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Zulip/4.0.3 Chrome/66.0.3359.181 Electron/3.1.10 Safari/537.36'), (True, True, False))
+
+        # Verify what happens if DESKTOP_MINIMUM_VERSION < v < DESKTOP_WARNING_VERSION
+        with mock.patch('zerver.views.compatibility.DESKTOP_MINIMUM_VERSION', '4.0.3'):
+            self.assertEqual(is_outdated_desktop_app('ZulipElectron/4.0.3 Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Zulip/4.0.3 Chrome/66.0.3359.181 Electron/3.1.10 Safari/537.36'), (True, False, False))
+
+        self.assertEqual(is_outdated_desktop_app('ZulipElectron/5.0.0 Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_3) AppleWebKit/537.36 (KHTML, like Gecko) Zulip/4.0.3 Chrome/66.0.3359.181 Electron/3.1.10 Safari/537.36'), (False, False, False))
 
         self.assertEqual(is_outdated_desktop_app('Mozilla/5.0 (Windows NT 6.1; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/79.0.3945.130 Safari/537.36'), (False, False, False))
 
diff --git a/zerver/views/compatibility.py b/zerver/views/compatibility.py
index f54b60546c..368f6822de 100644
--- a/zerver/views/compatibility.py
+++ b/zerver/views/compatibility.py
@@ -6,6 +6,7 @@ from django.utils.translation import ugettext as _
 
 from zerver.lib.response import json_error, json_success
 from zerver.lib.user_agent import parse_user_agent
+from version import DESKTOP_MINIMUM_VERSION, DESKTOP_WARNING_VERSION
 
 def pop_numerals(ver: str) -> Tuple[List[int], str]:
     match = re.search(r'^( \d+ (?: \. \d+ )* ) (.*)', ver, re.X)
@@ -89,7 +90,7 @@ def check_global_compatibility(request: HttpRequest) -> HttpResponse:
     return json_success()
 
 def is_outdated_desktop_app(user_agent_str: str) -> Tuple[bool, bool, bool]:
-    # Returns (insecure, banned, auto_update_broken
+    # Returns (insecure, banned, auto_update_broken)
     user_agent = parse_user_agent(user_agent_str)
     if user_agent['name'] == 'ZulipDesktop':
         # The deprecated QT/webkit based desktop app, last updated in ~2016.
@@ -105,7 +106,11 @@ def is_outdated_desktop_app(user_agent_str: str) -> Tuple[bool, bool, bool]:
         # distinguish those from modern releases.
         return (True, True, True)
 
-    if version_lt(user_agent['version'], '4.0.3'):
+    if version_lt(user_agent['version'], DESKTOP_MINIMUM_VERSION):
+        # Below DESKTOP_MINIMUM_VERSION, we reject access as well.
+        return (True, True, False)
+
+    if version_lt(user_agent['version'], DESKTOP_WARNING_VERSION):
         # Other insecure versions should just warn.
         return (True, False, False)