Dynamic Backpressure is a highly desirable family of routing protocols known for their attractive mathematical proprieties. However, these protocols suffer from a high end-to-end delay making them inefficient for real-time traffic with strict endto-end delay requirements. In this paper, we address this issue by proposing a new adjustable and fully distributed Backpressurebased scheme with low queue management complexity, named LifeTime-Aware BackPressure (LTA-BP). The novelty in the proposed scheme consists in introducing the urgency level as a new metric for service differentiation among the competing traffic flows in the network. Our scheme not just significantly improves the quality of service provided for real-time traffic with stringent end-to-end delay constraints, but interestingly protects also the flows with softer delay requirements from being totally starved. The proposed scheme has been evaluated and compared against other state of the art routing protocol, using computer simulation, and the obtained results show its superiority in terms of the achieved end-to-end delay and throughput.