Direct methods of image registration work by defining a measure of the difference between two images and using numerical optimization methods to find the transformation that minimizes the difference. It has often been proposed that these methods may be speeded up by using only a sub- set of pixels to compute the difference measure. Previous work has suggested some criteria to use in pixel selection based on the derivative of the image, but has not addressed the issue of performance degradation that can result from applying these techniques. In this paper, we show that un- less applied carefully, these methods do not actually help. Specifically, reliability of the registration algorithm is lost if the initial starting position is further from the optimum than the scale of the derivative. Additionally, we propose new criteria for pixel selection which are strongly based on in- formation theory, and are faster to compute. We verify these propositions for two popular image difference measures by examining their behavior as the transformation parameters are varied, and by registering a number of typical images.