The present simulation study examined the statistical properties (namely, Type I error and statistical power) of various novel randomized single-case multiple-baseline designs and associated randomized-test analyses for comparing the A- to B-phase immediate abrupt outcome changes in two independent intervention conditions. It was found that with at least 4 cases randomly assigned to each of the conditions, the procedures were generally sufficiently powerful to detect moderate effect-size differences between the two conditions. Two procedures based on matching the cases' intervention stagger positions and start points in the two conditions possessed the most rigorous design features while exhibiting power that was comparable to that of the other procedures, and therefore were highly recommended for consideration by two-sample intervention researchers working with limited resources.