A strategy for overcoming problems with the Rasch model's inability to handle missing data involves a pairwise algorithm which manipulates the data matrix to separate out the information needed for the estimation of item difficulty parameters in a test. The method of estimation compares two or three items at a time, separating out the ability parameters of the set of persons tested by means of conditional probability, to avoid biasing the difficulty parameters. To describe the difficulty of a set of items, a matrix is constructed in which each element is the number of people who responded correctly to one item and incorrectly to another item. The matrix of observations need not be complete. An analogous matrix is prepared to describe the relative abilities of the persons, by considering them two at a time and looking only at those items which one got right and the other got wrong. Maximum likelihood estimation and tests for fit of the parameter estimates are examined. (CM)