One or more embodiments describe a decision feedback equalizer for highly spectrally efficient communications. A method may be performed in a decision feedback equalizer (DFE). The method may include initializing values of tap coefficients of the DFE based on values of tap coefficients of a partial response filter through which said transmitted symbols passed en route to said sequence estimation circuit. The method may include receiving estimates of transmitted symbols from a sequence estimation circuit, and receiving an error signal that is generated based on an estimated partial response signal output by the sequence estimation circuit. The method may include updating values of tap coefficients of the DFE based on the error signal and the estimates of transmitted symbols. The method may include generating one or more constraints that restrict the impact of the error signal on the updating of the values of the tap coefficients of the DFE.