In this paper we discuss the problem of interface synthesis for a system on a chip (SoC) such that the power consumption is minimized under some given latency constraints. Since the AMBA protocol has become one of the standard interfaces for SoC cores, we develop our interface synthesis methods around the AMBA protocol. We first provide an analysis of the parameters of the AMBA bus and the communication protocols and a bus power model that will be used by various transformations. Several latency improving and power minimizing transformations are presented at the bus level. Finally, a heuristic is presented which applies the above transformations in a certain order to provide minimum power under a given latency constraint. Experimental results are reported on two example benchmarks in that show that the heuristic is able to reduce power consumption on the wires by about 28% on the average from an initial design having a single layer bus architecture.