RPL is an open routing protocol standardized by the ROLL group of IETF for constrained IP smart objects. It is one of the emergent protocols dedicated for Low Power and Lossy Networks (LLNs). Unfortunately, RPL su↵ers from significant packet loss due to the instability of the routes, and from a poor updates. Most of the existing solutions dedicated to solve the routes instability are based on improving the met-rics used for constructing the routes. Generally these metrics are based on some evaluation of the radio link quality. In this paper, we adopt a new approach for addressing route instability in RPL, by placing an additional constraint on the maximum number of children a node can accept during tree construction. We call our solution Bounded Degree RPL (BD-RPL). BD-RPL addresses the absence of updating in the downward routes construction. Technically, we use the existing control messages provided by RPL for bounding the node degrees, as well as for updating the downward routes. Therefore, BD-RPL does not generate any additional overhead compared to RPL. Also, BD-RPL does not depend on the radio link quality metric. That is, any improvement of the metric used for RPL will automatically yield an improvement for BD-RPL. We have evaluated BD-RPL using the Cooja simulator, and implemented it on the Iot-lab platform. The experimentation demonstrates an improvement over RPL by an average of 10% in packet delivery, 50% in energy consumption, and 60% in delay.