A key component in coherent underwater acoustic communication systems is an adaptive equalizer capable of tracking changes in the acoustic environment. The computation requirements of this equalizer can be very high, requiring substantial computation hardware and high power consumption. Several techniques have been devised for reducing the computational load of the equalizer by exploiting structure in the acoustic environment. In essence, these methods trade equalizer decoding performance for computational efficiency by reducing the number of equalizer parameters, the complexity of the update algorithm, or the rate of parameter updating. In this paper, a generalized equalizer model is developed combining several such complexity reduction techniques. From this viewpoint, the potential and limitations of each technique are discussed. Results are presented showing that computation savings in excess of an order of magnitude are possible.