In humid environments, decoupling the latent and sensible cooling loads - dehumidifying - can significantly improve chiller efficiency. Here, a basic limit for dehumidification efficiency is established from fundamental thermodynamics. This is followed by the derivation of how this limit is modified when the pragmatic constraint of a finite flux must be accommodated. These limits allow one to identify promising system modifications, and to quantify their impact. The focus is on vacuum-based membrane dehumidification. New high-efficiency configurations are formulated, most notably, by coupling pumping with condensation. More than an order-of-magnitude improvement in efficiency is achievable. It is contingent on water vapor exiting at its saturation pressure rather than at ambient pressure. Sensitivity studies to recovery ratio, temperature, relative humidity and membrane selectivity are also presented.