Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch's approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness of Rasch's approach for several important testing problems through simulation studies. Our Monte Carlo methodology is shown to compare favorably to other Monte Carlo methods proposed for this problem in two respects: it is considerably faster and it provides more reliable estimates of the Monte Carlo standard error.