It has previously been shown that the combined use of fair queuing and admission control would allow the Internet to provide satisfactory quality of service for both streaming and elastic flows without explicitly identifying traffic classes. In this paper we discuss the design of the required measurement based admission control (MBAC) scheme. The context is different to that of previous work on MBAC in that there is no prior knowledge of flow characteristics and there is a twofold objective: to maintain adequate throughput for elastic flows and to ensure low packet latency for any flow whose peak rate is less than a given threshold. In the paper we consider the second objective assuming realistically that most elastic and streaming flows are rate limited. We propose a MBAC algorithm and evaluate its performance by simulation under different stationary traffic mixes and in a flash crowd scenario. The algorithm is shown to offer a satisfactory compromise between flow performance and link utilization.