Randomization tests for alternating treatments designs, multiple baseline designs, and withdrawal/reversal designs are well-established. Recent classifications, however, also mention the "changing criterion design" as a fourth important type of single-case experimental design. In this paper, we examine the potential of randomization tests for changing criterion designs. We focus on the rationale of the randomization test, the random assignment procedure, the choice of the test statistic, and the calculation of randomization test p-values. Two examples using empirical data and an R computer program to perform the calculations are provided. We discuss the problems associated with conceptualizing the changing criterion design as a variant of the multiple baseline design, the potential of the range-bound changing criterion design, experimental control as an all-or-none phenomenon, the necessity of random assignment for the statistical-conclusion validity of the randomization test, and the use of randomization tests in nonrandomized designs.