A general tight-binding total-energy (TBTE) method is presented that accurately predicts energy differences caused by small perturbations such as those occurring in the evaluation of elastic constants and phonon spectra as well as energy differences from large changes in structure such as structural energy differences, equations of state, and defect energies. Unlike other quantitative TBTE models, no pair potential is required. In addition, we only fit to the band structure and total energies obtained from fcc and bcc first-principles calculations, although we could fit to other data as needed. We have applied the method to 11 transition and noble metals and obtained elastic constants, phonon spectra, and vacancy formation energies in very good agreement with both local-density theory and experiment.