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This paper proposes medium contention aware routing schemes for rate-constrained traffic in wireless sensor networks (WSNs) that maximize network lifetime. Three sufficient conditions, referred to as rate-based, degree-based, and mixed constraints, are incorporated into the routing formulations to guarantee medium access feasibility of the routing solutions. Simulations show that the mixed condition based approach always achieves better network lifetimes than the other two approaches for larger networks, but at the cost of larger execution times. Our results show that the rate-based condition approach is the best choice in terms of balancing between solution quality and complexity.