OFDM renders multipath channels with finite memory equivalent to parallel flat fading subchannels, over which equalization amounts to simple phase compensation. If the channel status information is known at the transmitter side, optimal power loading across subchannels is possible. Users mobility, time and carrier asynchronism introduce variations in the equivalent channel impulse response setting the channel coherence time as a boundary for the OFDM symbol duration. Optimal design should incorporate such variations, possibly avoiding the overhead of frequent training. Most adaptive modulation schemes assume knowledge of the channel response and flat fading. Modeling the channel taps as correlated Gaussian random processes, we develop the optimal power/bit loading strategies for frequency selective fading, based on the knowledge of the channel past estimates and correlation. In practice the channel sample correlation are obtained as a by-product of channel estimation which, however, does not need to be performed on a block by block basis.