Blind equalization in noisy multiuser channels has met with increasing attention with the advent of multiaccess digital communication systems. We examine blind equalizer performance in cases where perfect equalization proves unattainable due to noise and interference from concurrent users. In particular, we obtain a characterization of stationary points and extrema for a family of blind criteria in "undermodeled" cases, which assimilates the influence of differing source statistics and background noise correlation properties; relations to mean-square equalization measures are then obtained as a byproduct. By re-examining a gradient search procedure, we obtain domains of attraction of each extremum in a special "sufficient order" setting. We also derive a global step-size bound for undermodeled cases, which ensures convergence of a gradient search procedure to an extremum of a blind cost function. We likewise confirm that the super-exponential algorithm results from an optimal choice of this step-size parameter