AbstractDesign efficiencies are studied for inferences regarding the coefficients of second‐order models. Subspaces of parameters are identified wherein each of two designs dominates the other locally, or the two designs are equally efficient. Both Fisher efficiency in estimation and Pitman efficiency in hypothesis testing are considered. Eight small second‐order designs ink=3 regressor variables are screened using a four‐part efficiency index. Of these, the central composite, Box‐Behnken, small composite, and hybrid H310 and H311 B designs are found to be generally superior and roughly comparable. Detailed comparisons among these five designs are then undertaken. This work provides further tools for use in design evaluation, requiring only basic matrix operations independently of experiment