As commonplace speech-enabled devices are getting smaller and lighter, we are faced with a need for simpler processing and simpler hardware. In this talk I will present some alternative ways to approach multi-channel and single-channel speech enhancement under these constraints. More specifically, I will talk about new ways to formulate beamforming that are numerically more lightweight, and operate best when using physically compact arrays, and then I will discuss single-channel approaches using a deep network which, in addition to imposing a lightweight computational load, are amenable to aggressive hardware optimizations that can result in massive power savings and reductions in hardware footprint.