Light-Fidelity (LiFi) has emerged in the last few years as a promising technology for alleviating the stringent demand for wireless data services. Prior works have considered LiFi operating either in the visible light or infrared spectrum. Each spectrum band has its own advantages: visible light allows leveraging existing infrastructure for communication, while infrared is not affected by light dimming. In this work, we propose a modulation scheme that retains the benefits of both bands, introducing a simple, low-cost, yet efficient dimming solution for LiFi networks. We compare the performance of the proposed dimming scheme with both the digital and analog dimming techniques traditionally used in LiFi systems. Simulation results show that our dimming solution offers better communication and illumination performance than previous proposals, providing larger signal-to-noise ratio, spectral efficiency, and a full and fine-grained dimming range. Finally, we prototype our solution by designing an extended version of the OpenVLC 1.3 platform, and we experimentally show its robust communication performance under different dimming conditions. We make the implemented system publicly available to the research community.