diff --git a/scripts/restart-server b/scripts/restart-server
index fe685bd968..d35eeefcf1 100755
--- a/scripts/restart-server
+++ b/scripts/restart-server
@@ -29,6 +29,12 @@ logging.basicConfig(format=f"%(asctime)s {action}-server: %(message)s", level=lo
 
 parser = argparse.ArgumentParser()
 parser.add_argument("--fill-cache", action="store_true", help="Fill the memcached caches")
+if action == "restart":
+    parser.add_argument(
+        "--less-graceful",
+        action="store_true",
+        help="Restart with more concern for expediency than minimizing availability interruption",
+    )
 args = parser.parse_args()
 
 deploy_path = os.path.realpath(os.path.join(os.path.dirname(__file__), ".."))
@@ -47,10 +53,6 @@ if args.fill_cache:
     logging.info("Filling memcached caches")
     subprocess.check_call(["./manage.py", "fill_memcached_caches"])
 
-core_server_services = ["zulip-django"]
-if os.path.exists("/etc/supervisor/conf.d/zulip/thumbor.conf"):
-    core_server_services.append("zulip-thumbor")
-
 current_symlink = os.path.join(DEPLOYMENTS_DIR, "current")
 last_symlink = os.path.join(DEPLOYMENTS_DIR, "last")
 change_symlink = os.readlink(current_symlink) != deploy_path
@@ -61,11 +63,57 @@ if change_symlink:
 config_file = get_config_file()
 tornado_ports = get_tornado_ports(config_file)
 
-# We restart just the zulip-tornado service early, in order to
+# Start by restarting the workers and similar processes, one at a
+# time.  Workers can always support processing events with old event
+# contents, but cannot necessarily understand events enqueued by a
+# newer Django process.  Restarting them one at a time, rather than
+# all-at-once, minimizes the downtime of each, and reduces startup
+# contention.
+#
+# For "start" or less-graceful circumstances, we don't need to
+# iterate; we'll stop all of them at once, and start them all later.
+# In those cases, using the glob form is faster -- but if we do need
+# to iterate, we need to expand the glob.
+if action == "start" or args.less_graceful:
+    workers = ["zulip-workers:*"]
+else:
+    worker_status = subprocess.run(
+        ["supervisorctl", "status", "zulip-workers:*"],
+        universal_newlines=True,
+        stdout=subprocess.PIPE,
+    )
+    # `supercisorctl status` returns 3 if any are stopped, which is fine here.
+    if worker_status.returncode not in (0, 3):
+        worker_status.check_returncode()
+    workers = [status_line.split()[0] for status_line in worker_status.stdout.splitlines()]
+
+if os.path.exists("/etc/supervisor/conf.d/zulip/thumbor.conf"):
+    workers.append("zulip-thumbor")
+if os.path.exists("/etc/supervisor/conf.d/zulip/zulip_db.conf"):
+    workers.append("process-fts-updates")
+
+if action == "restart":
+    if args.less_graceful:
+        # The less graceful form stops every worker now; we start them
+        # back up at the end.
+        logging.info("Stopping workers")
+        subprocess.check_call(["supervisorctl", "stop", *workers])
+    else:
+        # We cannot pass all of these to one `supervisorctl restart`
+        # because that takes them all down at once, waits until they are
+        # all down, and then brings them back up; doing them sequentially
+        # requires multiple `supervisorctl restart` calls.
+        for worker in workers:
+            logging.info("Restarting %s", worker)
+            subprocess.check_call(["supervisorctl", "restart", worker])
+
+# Next, we restart the Tornado processes sequentially, in order to
 # minimize downtime of the tornado service caused by too many Python
-# processes restarting at the same time resulting in it receiving
+# processes restarting at the same time, resulting in each receiving
 # insufficient priority.  This is important, because Tornado is the
 # main source of user-visible downtime when we restart a Zulip server.
+# We do this before restarting Django, in case there are new event
+# types which it will need to know how to deal with.
 if len(tornado_ports) > 1:
     for p in tornado_ports:
         # Restart Tornado processes individually for a better rate of
@@ -78,26 +126,22 @@ else:
     logging.info("%s Tornado process", verbing)
     subprocess.check_call(["supervisorctl", action, "zulip-tornado", "zulip-tornado:*"])
 
-# Restart the uWSGI and related processes via supervisorctl.
-if action == "restart":
-    logging.info("Stopping workers")
-    subprocess.check_call(["supervisorctl", "stop", "zulip-workers:*"])
-    logging.info("Stopping server core")
-    subprocess.check_call(["supervisorctl", "stop", *core_server_services])
+# Finally, restart the Django uWSGI processes.
+logging.info("%s django server", verbing)
+subprocess.check_call(["supervisorctl", action, "zulip-django"])
 
-logging.info("Starting server core")
-subprocess.check_call(["supervisorctl", "start", *reversed(core_server_services)])
-logging.info("Starting workers")
-subprocess.check_call(["supervisorctl", "start", "zulip-workers:*"])
+# If we were doing this non-gracefully, or starting as opposed to
+# restarting, we need to turn the workers (back) on.  There's no
+# advantage to doing this not-all-at-once.
+if action == "start" or args.less_graceful:
+    logging.info("Starting workers")
+    subprocess.check_call(["supervisorctl", "start", *workers])
 
 using_sso = subprocess.check_output(["./scripts/get-django-setting", "USING_APACHE_SSO"])
 if using_sso.strip() == b"True":
     logging.info("Restarting Apache WSGI process...")
     subprocess.check_call(["pkill", "-f", "apache2", "-u", "zulip"])
 
-if os.path.exists("/etc/supervisor/conf.d/zulip/zulip_db.conf"):
-    subprocess.check_call(["supervisorctl", action, "process-fts-updates"])
-
 logging.info("Done!")
 print(OKGREEN + f"Zulip {action}ed successfully!" + ENDC)