Delay-Constrained Routing (DCR) problems require to route a new flow in a computer network subject to worst-case end-to-end delay guarantees. The delay of a packet flow has three components, one of which is the "queueing delay", that depends on the scheduling algorithm implemented by the routers of the network. When flows are not independent of each other, i.e., admitting a new flow changes the delay of the existing ones, admission control policies are necessary to ensure that existing flows do not become latency-unfeasible. It has been recently shown that admission control runs contrary to the usual objective function employed in these models, i.e., minimization of the reserved rates, significantly worsening network performance. In this paper we investigate the phenomenon and propose a heuristic way to overcome the problem.