diff --git a/tonic/src/codec/decode.rs b/tonic/src/codec/decode.rs
index 8cba8ba88..18412d733 100644
--- a/tonic/src/codec/decode.rs
+++ b/tonic/src/codec/decode.rs
@@ -285,6 +285,9 @@ impl StreamingInner {
         if let Direction::Response(status) = self.direction {
             if let Err(e) = crate::status::infer_grpc_status(self.trailers.as_ref(), status) {
                 if let Some(e) = e {
+                    // If the trailers contain a grpc-status, then we should return that as the error
+                    // and otherwise stop the stream (by taking the error state)
+                    self.trailers.take();
                     return Err(e);
                 }
             }