A predictive tool for the design of new, higher temperature superconductors requires a simple, first-principles technique based on well-established axioms as embodied in Density Functional Theory (DFT), without post-calculation corrections or increased levels of complexity. We show that anomalies in the calculated phonon dispersions of compounds with AlB 2 -type structures are good descriptors of their superconducting transition temperatures. This ab initio methodology has proven robust for descriptions of: the superconductivity of MgB 2 and other related AlB 2 -type structures, the different isotopic forms of MgB 2 , a series of substituted MgB 2 compositions with Al and with transition metals, the pressure dependence of the superconductivity of MgB 2 and various temperature effects. Calculated values are well correlated with experimentally determined values within experimental errors, when sufficiently fine k-grids are used to resolve Fermi surface details. This methodology provides invaluable insight on the mechanisms of superconductivity, can be extended to other crystal systems and has been used to predict superconducting T c for new compounds.