From the authors’ abstract: Steiner and non-Steiner 2-\((v,3)\) trades of minimum volume are considered. It is shown that these trades are composed of a union of some Pasch configurations and possibly some 2-\((v',3)\) trades with \(6\leq v'\leq 10\). We determine the number of non-isomorphic Steiner 2-\((v,3)\) trades of minimum volume. As for non-Steiner trades the same is done for all \(v\), except for \(v\equiv 5\pmod 6\).