diff --git a/bugsnag/delivery.py b/bugsnag/delivery.py
index acd2da2..6dc8cd0 100644
--- a/bugsnag/delivery.py
+++ b/bugsnag/delivery.py
@@ -93,7 +93,6 @@ def deliver_sessions(self, config, payload: Any, options=None):
                 options = {}
 
             options['endpoint'] = config.session_endpoint
-            options['success'] = 202
 
             self.deliver(config, payload, options)
 
@@ -151,10 +150,14 @@ def request():
             status = resp.getcode()
 
             if 'success' in options:
-                success = options['success']
+                # if an expected status code has been given then it must match
+                # exactly with the actual status code
+                success = status == options['success']
             else:
-                success = 200
-            if status != success:
+                # warn if we don't get a 2xx status code by default
+                success = status >= 200 and status < 300
+
+            if not success:
                 config.logger.warning(
                     'Delivery to %s failed, status %d' % (uri, status)
                 )
@@ -184,12 +187,16 @@ def request():
 
             response = requests.post(uri, **req_options)
             status = response.status_code
+
             if 'success' in options:
-                success = options['success']
+                # if an expected status code has been given then it must match
+                # exactly with the actual status code
+                success = status == options['success']
             else:
-                success = requests.codes.ok
+                # warn if we don't get a 2xx status code by default
+                success = status >= 200 and status < 300
 
-            if status != success:
+            if not success:
                 config.logger.warning(
                     'Delivery to %s failed, status %d' % (uri, status)
                 )