This catalogue of small incomplete factorial designs was compiled to provide designs for two- and three-level factors with 20 or fewer runs. It is assumed that the three-level factors are quantitative. The designs are suitable for estimating a selection of interactions, including the linear-by-linear components of interactions between the three-level factors. Ad hoc methods were used to construct the designs, so that there is no particular uniformity in the designs and no general property of optimality which they satisfy. Designs were selected on the basis of a measure of efficiency which is presented. No claim is made that the given designs are the best possible, and others should be encouraged to try to develop more efficient designs. A detailed example based on a real experiment is presented.