The graded response model for two-stage testing was applied to an attitudes toward science scale using real-data simulation. The 48-item scale was administered to 920 students at a grade-8 equivalent in Singapore. A two-stage 16-item computerized adaptive test was developed. In two-stage testing an initial, or routing, test is followed by a second-stage testlet of greater or lesser difficulty based on performance. A conventional test of the same length as the adaptive two-stage test was selected from the 48-item pool. Responses to the conventional test, the routing test, and a testlet were simulated. The algorithm of E. Balas (1965) and the multidimensional knapsack problem of optimization theory were used in test development. The simulation showed the efficiency and accuracy of the two-stage test with the graded response model in estimating attitude trait levels, as evidenced by better results from the two-stage test than its conventional counterpart and the reduction to one-third of the length of the original measure. Six tables and three graphs are included. (SLD)