This paper discusses the use of latent class structure as a modelling framework for tests in which much of the data conforms to a relatively small number of systematic patterns. Application of this framework to the analysis of tests has been limited because available parameter estimation algorithms can only handle a relatively small number of items. This paper proposes a modification of the constrained maximum likelihood estimation algorithm of tests with many more items. A number of special cases of the latent class structure model and a series of problems which arise in the development of any latent class model are reviewed and discussed. A few problems with no satisfactory general solution are noted. The proposed procedures are used to develop and test models for signed-number addition test data gathered by Tatsuoka and Birenbaum. The models are shown to represent most features of the data well, including some significantly negative interitem correlations and differences between groups in covariance structure. The ability of these simple models to represent non-unidimensional data, and to represent differences between groups in covariance structure and means simultaneously, suggests that the latent class structure framework may be very useful in dealing with a number of troublesome psychometric issues. (Author/JAZ)