Within a dynamical approach, the average spins of fission fragments originating from the 12C + 235,236U and 13C + 235U complete fusion reactions at c.m. energies in the range of Ec.m. = (55–75) MeV are analyzed as a function of energy. Particular attention is given to the process of formation of initial distributions for the components of the total angular momentum of compound nuclei. It is shown that substantial distinctions in the behavior of average spins of fission fragments for different fusion reaction channels are expected to be observed in the range of subbarrier energies.