The maximum possible volume of a simple, non-Steiner \((v, 3, 2)\) trade was determined for all \(v\) by Khosrovshahi and Torabi (Ars Combinatoria \(51 (1999), 211-223)\); except that in the case \(v \equiv 5\) (mod 6), \(v \geq 23\), they were only able to provide an upper bound on the volume. In this paper we construct trades with volume equal to that bound for all \(v \equiv 5\) (mod 6), thus completing the problem.