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We propose a new method that uses an iterative closest point (ICP) algorithm to fit three-dimensional points to a prior geometric model for the purpose of determining the position and orientation (pose) of a sensor with respect to a model. We use a method similar to the Random Sample and Consensus (RANSAC) algorithm. However, where RANSAC uses random samples of points in the fitting trials, DIRSAC DIRects the sampling by ordering the points according to their contribution to the solution constraints. This is particularly important when the data is quasi-degenerate; meaning that some of the degrees of freedom of the pose are under constrained. In this case, the standard RANSAC algorithm often fails to find the correct solution. Our approach uses mutual information to avoid redundant points that result in degenerate sample sets. We demonstrate our approach on real data and show that in the case of quasi-degenerate data, the proposed algorithm outperforms RANSAC. [ABSTRACT FROM AUTHOR]