Illumination LEDs, but also infrared LEDs have limited bandwidth. To achieve high throughput, one needs to modulate the LED significantly above its 3 dB bandwidth. Orthogonal Frequency Division Multiplexing (OFDM) is a popular modulation technique to cope with the frequency selectivity of the LED channel. In this article, we challenge whether its large Peak-to-Average-Power Ratio (PAPR) and resulting large DC bias are justified. We compare systems using the same power and derive how PAM and OFDM variants reach their optimum throughput at different bandwidths and differently shaped spectral densities, thus at very different Signal to Noise Ratio (SNR) profiles but nonetheless the same transmit power.When corrected for the path loss and normalized to the noise power in the 3 dB bandwidth of the LED, we call this the Normalized Power Budget (NPB). OFDM can exploit the low-pass LED response using a waterfilling approach. This is attractive if the NPB exceeds 60 dB. OFDM will then have to spread its signal over more than ten times the LED bandwidth and requires a DC bias of more than 4 times the rms modulation depth. Second-order distortion and LED droop may then become a limitation, if not compensated. At lower power (NPB between 30 and 60 dB), DCO-OFDM outperforms PAM, provided that it significantly reduces its bias and only if it uses an appropriate adaptive bit and power loading. Without adaptive bit loading, thus using a frequency–constant modulation order, for instance made feasible by a pre-emphasis, OFDM always shows lower performance than PAM; about 2.5 dB at a NPB around 60 dB. Below 30 dB of NPB, even waterfilling cannot outweigh the need for a larger bias in OFDM, and PAM should be preferred. We argue that a mobile system that has to operate seamlessly in wide coverage and short–range high–throughput regimes, needs to adapt not only its bandwidth and its bit–loading profile, but also its DCO-OFDM modulation depth, and preferably falls back from OFDM to PAM.