Algorithms described in the literature for adaptation of equalizers usually consider minimization of a mean square cost. The mean square cost considered is usually comprised of two components; one component is the mean square error which arises because of inexact equilization of the channel response to the desired response. The other component can be identified as the mean square value of the noise at the output of the equalizer which is generated by channel noise. The paper describes algorithms which enable the two components to be independently weighted and the weighted mean square error minimized by the adaptive algorithms. Motivation for considering the independent weight is discussed in relation to the use of a compromised Viterbi algorithm receiver for the recovery of digital data transmitted over a noisy dispersive channel. However, other applications also exist.