LEDs, particularly those used for Visible Light Communications (VLC), have a limited bandwidth, while above their 3 dB bandwidth, the roll-off is relatively gentle. If the modulation bandwidth would be limited to the 3 dB LED bandwidth, the achievable rate would be unacceptably constrained. Hence, effective communication systems need to optimize the use of bandwidth significantly above this 3 dB point. Orthogonal Frequency Division Multiplexing (OFDM) is a popular method to fine-tune the amount of power and constellation as a function of the channel response over different frequencies. Various power and bit loading strategies have been proposed and simulated in literature, but their performance was not captured in expressions. This manuscript derives these for optimal waterfilling, uniform and pre-emphasized power loading for the LED channel, that severely attenuates high frequencies. We also investigate the influence of practical discrete constellations and verify our new results experimentally. Interestingly, simple uniform loading only falls less than 1∼2% short of the throughput achieved by waterfilling, but when we restrict OFDM to discrete QAM constellation sizes, the penalty for uniform loading is 1.5 dB. Inspired by the good performance of uniform power loading, we propose an algorithm to find the best discrete bit loading for uniform power within an optimized band. As pre-emphasis is nonetheless attractive because a flattened channel does not need adaptive sub-carrier loading, we quantify its penalty. This can be modest provided that the system can adapt its transmit bandwidth, thereby adaptively switching upper sub-carriers to zero power.