diff --git a/notebook/notebookapp.py b/notebook/notebookapp.py
index b0c2d3150..98c7332b0 100644
--- a/notebook/notebookapp.py
+++ b/notebook/notebookapp.py
@@ -790,11 +790,11 @@ class NotebookApp(JupyterApp):
         help="Reraise exceptions encountered loading server extensions?",
     )
 
-    iopub_msg_rate_limit = Float(0, config=True, allow_none=True, help="""(msg/sec)
+    iopub_msg_rate_limit = Float(0, config=True, help="""(msg/sec)
         Maximum rate at which messages can be sent on iopub before they are
         limited.""")
 
-    iopub_data_rate_limit = Float(0, config=True, allow_none=True, help="""(bytes/sec)
+    iopub_data_rate_limit = Float(0, config=True, help="""(bytes/sec)
         Maximum rate at which messages can be sent on iopub before they are
         limited.""")
 
diff --git a/notebook/services/kernels/handlers.py b/notebook/services/kernels/handlers.py
index 9a7a33a7c..afadecd34 100644
--- a/notebook/services/kernels/handlers.py
+++ b/notebook/services/kernels/handlers.py
@@ -196,15 +196,14 @@ class ZMQChannelsHandler(AuthenticatedZMQStreamHandler):
         self._kernel_info_future = Future()
 
         # Rate limiting code
-        self._iopub_msg_count = 0
-        self._iopub_byte_count = 0
+        self._iopub_window_msg_count = 0
+        self._iopub_window_byte_count = 0
         self._iopub_msgs_exceeded = False
         self._iopub_data_exceeded = False
-        # Queue of (time stamp, delta)
-        # Allows you to specify that the msg or byte counts should be adjusted
+        # Queue of (time stamp, byte count)
+        # Allows you to specify that the byte count should be lowered
         # by a delta amount at some point in the future.
-        self._queue_msg_count = []
-        self._queue_byte_count = []
+        self._iopub_window_byte_queue = []
 
     @gen.coroutine
     def pre_get(self):
@@ -284,40 +283,31 @@ class ZMQChannelsHandler(AuthenticatedZMQStreamHandler):
         if channel == 'iopub':
     
             # Remove the counts queued for removal.
-            while len(self._queue_msg_count) > 0:
-                queued = self._queue_msg_count[0]
-                if (IOLoop.current().time() >= queued[0]):
-                    self._iopub_msg_count += queued[1]
-                    del self._queue_msg_count[0]
-                else:
-                    # This part of the queue hasn't be reached yet, so we can
-                    # abort the loop.
-                    break
-
-            while len(self._queue_byte_count) > 0:
-                queued = self._queue_byte_count[0]
-                if (IOLoop.current().time() >= queued[0]):
-                    self._iopub_byte_count += queued[1]
-                    del self._queue_byte_count[0]
+            now = IOLoop.current().time()
+            while len(self._iopub_window_byte_queue) > 0:
+                queued = self._iopub_window_byte_queue[0]
+                if (now >= queued[0]):
+                    self._iopub_window_byte_count -= queued[1]
+                    self._iopub_window_msg_count -= 1
+                    del self._iopub_window_byte_queue[0]
                 else:
                     # This part of the queue hasn't be reached yet, so we can
                     # abort the loop.
                     break
                     
             # Increment the bytes and message count
-            self._iopub_msg_count += 1
+            self._iopub_window_msg_count += 1
             byte_count = sum([len(x) for x in msg_list])
-            self._iopub_byte_count += byte_count
+            self._iopub_window_byte_count += byte_count
             
             # Queue a removal of the byte and message count for a time in the 
             # future, when we are no longer interested in it.
-            self._queue_msg_count.append((IOLoop.current().time() + self.limit_window, -1))
-            self._queue_byte_count.append((IOLoop.current().time() + self.limit_window, -byte_count))
+            self._iopub_window_byte_queue.append((now + self.limit_window, byte_count))
             
             # Check the limits, set the limit flags, and reset the
             # message and data counts.
-            msg_rate = float(self._iopub_msg_count) / self.limit_window
-            data_rate = float(self._iopub_byte_count) / self.limit_window
+            msg_rate = float(self._iopub_window_msg_count) / self.limit_window
+            data_rate = float(self._iopub_window_byte_count) / self.limit_window
             
             # Check the msg rate
             if self.iopub_msg_rate_limit is not None and msg_rate > self.iopub_msg_rate_limit and self.iopub_msg_rate_limit > 0: