We consider visible light communication (VLC) using phosphorescent white light-emitting diodes (LEDs) and two different receiver types -a simple receiver for moderate data rate requirements and a sophisticated receiver for higher data rate requirements equipped with an optical blue filter. We address the question, whether it is viable to support both heterogeneous receiver types simultaneously, using a single LED-based transmitter, and characterize the trade-offs associated with a common waveform. In particular, with regard to a simplistic transmitter and receiver structure, we propose a "nested" pulse-position modulation (nPPM) scheme and show that it improves upon conventional time sharing, when the bit rate of the simple receiver is supposed to be retained, while realizing a higher bit rate for the sophisticated receiver. An analysis of the available signal-to-noise ratio at the receiver for a practical setting combined with analytical and simulated error performance results corroborates the feasibility of our approach. Furthermore, we devise an end-to-end signal model, which includes the electrical properties of the LED as well as interference effects associated with optical filtering, and assess the influence on the resulting error performance. Due to its simplicity, our nPPM scheme may be particularly relevant for future mass-market VLC deployments as well as for proprietary solutions.