A theory is presented to account for the wave energy in lower hybrid current drive experiments when the density threshold for decay into ion cyclotron quasi-mode is exceeded. Immediately above the threshold, convective losses dominate and discrete sidebands are excited. These sidebands have much larger wave-numbers, and strong minority ion heating is possible. Majority ion heating occurs, however, only at high power. At higher densities, ion Landau damping becomes important. The frequency spectrum is non-monotonic in this region with the minimum frequency determined by nonlinear coupling. Majority ion absorption is significant even at moderate power levels.