Simultaneous wireless information and power transfer (SWIPT) represents an enabling paradigm for future energy-sustainable networks. Multiple-input multiple-output (MIMO) technology enhances the performance of SWIPT systems via precoding. We typically rely on heuristic precoding designs in practice, due to their favorable performance-complexity balance, as opposed to their optimization-based counterparts. On the other hand, these designs provide limited flexibility. Furthermore, the standard precoding heuristics are SWIPT-agnostic. In this paper, we propose a novel MIMO precoding framework for SWIPT that is based on the notion of controllable residual interference to resolve the aforementioned issues. Specifically, we consider a multiple-input single-output (MISO) broadcast system for SWIPT with separate energy and information receivers. In this context, we formulate interference-constrained problems and apply a relaxation to obtain low-complexity solutions that admit closed-form expressions. We also extend our approach to hybrid precoding designs for the case where the base station adopts an analog/digital architecture due to particularly stringent cost and energy consumption constraints. Numerical simulations unveil the performance gains of the proposed precoding schemes over the solutions based on semi-definite relaxation (SDR) and heuristic baseline methods and provide valuable insights.