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This article treats the tree circuit synthesis problem for families F= {f1, f2, ···, fm} of Boolean functions fj of the same three variables. In addition to the development of criteria for determining the most economical of the three possible tree circuit decompositions: (j= 1, 2,···, m) of a given family, certain upper bounds BT(3, m) are obtaie···,d on the " tree circuit cost" T( F) of such a fmily; these have the property tha regardless of the mebers of F, the in-equality T(F)¿BT(3, m) holds and furthermore, a family Fists in which actualy attains this upper bound. These upper bounds or estimates are known to have a wide application in switching theory generally, and in particular in the theory of tree circuits and in the decomposition theory of Boolean functions.