To facilitate the search for new magnetic semiconductors with high transition temperatures T C , we use dynamical mean-field theory to evaluate T C for a double-exchange system with general angular momentum j = 1 / 2 , 3 / 2 , 5 / 2 , … . For simplicity, we assume that there is one local moment per site and that the Hund's coupling J c between the local moments and the charge carriers (with undoped bandwidth W ) is large. The maximum Curie temperature T C max ( m j , j ) for a given m j and j occurs when the m j sub-band is half-filled. For a fixed j, T C max ( m j , j ) is the largest in the lowest or the highest sub-band with m j = ± j , where the carriers are most optimally coupled to the local moments. When j ⪢ 1 , T C max ( ± j , j ) scales like W / 2 j + 1 , which is the bandwidth of each m j sub-band. For j = 1 / 2 , T C max ( ± 1 / 2 , 1 / 2 ) is suppressed by fluctuations of the carrier spin. Surprisingly, T C max ( ± j , j ) reaches a maximum for j = 3 / 2 , the same angular momentum as the charge carriers in p-band semiconductors like GaAs and Ge.