Comparing with hard real-time approach, (m,k)-firm constraint and its related scheduling policies are considered as an efficient way to increase the admission rate of real-time streams to a network thanks to the possibility to drop until k-m out of any k consecutive processing requirements, reducing thus the workload. Although it is interesting for probabilistic (m,k)-firm guarantee, we show however in this paper that for deterministic (m,k)-firm guarantee, reducing the workload by a factor of m/k does not contribute to reducing the resource requirement in general. So the relaxed (m,k)-firm constraint is proposed. The sufficient schedulability condition under non pre-emptive fixed priority scheduling is derived and its practical interest in terms of the resource requirement reduction is demonstrated.