diff --git a/codec-http2/src/main/java/io/netty/handler/codec/http2/DefaultHttp2RemoteFlowController.java b/codec-http2/src/main/java/io/netty/handler/codec/http2/DefaultHttp2RemoteFlowController.java
index 12feeceb80..04e4b19241 100644
--- a/codec-http2/src/main/java/io/netty/handler/codec/http2/DefaultHttp2RemoteFlowController.java
+++ b/codec-http2/src/main/java/io/netty/handler/codec/http2/DefaultHttp2RemoteFlowController.java
@@ -235,8 +235,10 @@ public class DefaultHttp2RemoteFlowController implements Http2RemoteFlowControll
     }
 
     /**
-     * This will allocate bytes by stream weight and priority for the entire tree rooted at {@code parent}, but does
-     * not write any bytes.
+     * This will allocate bytes by stream weight and priority for the entire tree rooted at {@code parent}, but does not
+     * write any bytes. The connection window is generally distributed amongst siblings according to their weight,
+     * however we need to ensure that the entire connection window is used (assuming streams have >= connection window
+     * bytes to send) and we may need some sort of rounding to accomplish this.
      *
      * @param parent The parent of the tree.
      * @param connectionWindow The connection window this is available for use at this point in the tree.
@@ -282,7 +284,10 @@ public class DefaultHttp2RemoteFlowController implements Http2RemoteFlowControll
                 int weight = child.weight();
                 double weightRatio = weight / (double) totalWeight;
 
-                int bytesForTree = Math.min(nextConnectionWindow, (int) Math.ceil(connectionWindow * weightRatio));
+                // In order to make progress toward the connection window due to possible rounding errors, we make sure
+                // that each stream (with data to send) is given at least 1 byte toward the connection window.
+                int connectionWindowChunk = Math.max(1, (int) (connectionWindow * weightRatio));
+                int bytesForTree = Math.min(nextConnectionWindow, connectionWindowChunk);
                 int bytesForChild = Math.min(state.streamableBytes(), bytesForTree);
 
                 if (bytesForChild > 0) {