Two iterative procedures for constructing Rasch scales are presented. A log-likelihood ratio test based on a quasi-loglinear formulation of the Rasch model is given by which one item at a time can be deleted from or added to an initial item set. In the so-called "top-down" algorithm, items are stepwise deleted from a relatively large initial item set, whereas in the "bottom-up" algorithm items are stepwise added to a relatively small initial item set. Both algorithms are evaluated through a simulation study with generated data. Item parameters are given for four generated unidimensional data sets and two generated two-dimensional sets. Abilities were randomly sampled from a multivariate normal distribution with a sample size of 1,000. Results for the top-down algorithm were poor, but results for the bottom-up algorithm were more encouraging. It is suggested that alternating the bottom-up algorithm with one or two iterations of the top-down algorithm would allow the procedure to reject items that were added incorrectly in a previous step. Eight tables illustrate the item parameters and the use of both algorithms for the generated data. (SLD)