The first dedicated algorithm to enumerate even-odd designs of strength 3 is presented. Such designs cannot be constructed by folding over smaller designs, but they may permit simultaneous estimation of many more two-factor interactions than designs that can be constructed by folding over. In the algorithm, enumeration is restricted to the computationally convenient class of designs with at least one nonzero correlation between a two-factor and a three-factor interaction contrast vector. All such designs with up to 56 runs, all those with 64 runs and up to 13 factors, and a specific subclass of those with 64 runs and more than 13 factors have been enumerated.1 The best ranked 64-run designs substantially improve on benchmark designs from the literature.