The role of a delay-constrained routing protocol is to find paths between senders and receivers subject to a delay constraint while eÆciently using network resources. Many delay-constrained routing protocols where proposed these last years, most of them give priority to cost minimization during path computing process. This approach builds paths with end-to-end delays too close to the delay constraint. We believe that such paths are risky because of the load variation and the imprecision of delay information in the network. In this paper we propose a new approach for delay-constrained routing which tries to find the best compromise between cost minimization and the risk level regarding the delay constraint. We first present PDCR, a Parameterised Delay-Constrained Routing protocol that implements our approach using a simple and eÆcient parameterised selection function. Then we propose three new delay-constrained multicast routing protocols based on source (Naive), destination (Greedy) and mixed multicast routing techniques. These pro- tocols use PDCR as the underline unicast routing algorithm. Simulation results show that our protocols produce paths and trees which are stable, less risky and suitable for different network conditions.