The spectral efficiency of L-branch selection diversity (SD) receiver with different adaptive transmission techniques operating over generalised-Gamma (GG) fading channels is studied. Novel expressions for important adaptive transmission techniques are obtained, namely optimal power and rate adaptation, optimal rate adaptation, channel inversion with fixed rate (CIFR) and truncated CIFR. Furthermore, simplified expressions for the capacities are obtained for SD reception in Nakagami-m as well as Weibull fading channels. The derived closed-from expressions extend previously published results to the GG fading model. Numerical results are given to demonstrate the usefulness of the theoretical approach.