This article studies the generation of test sets that consist of multi-cycle test cubes. Such test cubes have partially-specified scan-in states, and several functional clock cycles between scan operations. Test cubes are important for test data compression. In addition, multi-cycle tests can detect delay defects that are not detected by single-cycle tests. The use of multi-cycle test cubes is shown to reduce the number of test cubes required for detecting single stuck-at faults compared with the case where single-cycle test cubes are used. This article also shows that a multi-cycle test cube for a single stuck-at fault can have fewer specified scan-in values than a single-cycle test cube for the same fault. As a result, multi-cycle test cubes can be more effective for test data compression. This article also discusses the conditions under which multi-cycle test cubes can be merged in order to further reduce the number of test cubes in a test set.