The increasing viability of three dimensional (3D) silicon integration technology has opened new opportunities for chip design innovations, including the prospect of extending emerging systems-on-chip (SoC) design paradigms based on networks-on-chip (NoC) interconnection architectures to 3D chip designs. In this paper, we consider the problem of designing application-specific 3D-NoC architectures that are optimized for a given application. We present novel 3D-NoC synthesis algorithms that make use of accurate power and delay models for 3D wiring with through-silicon vias. In particular, we present a very efficient 3D-NoC synthesis algorithm called ripup-reroute-and-router-merging (RRRM), that is based on a rip-up and reroute formulation for routing flows and a router merging procedure for network optimization. Experimental results on 3D-NoC design cases show that our synthesis results can on average achieve a 74% reduction in power consumption and a 17% reduction in hop count over regular 3D mesh implementations and a 52% reduction in power consumption and a 17% reduction in hop count over optimized 3D mesh implementations.