The redshift and luminosity distributions of 36 Swift short gamma-ray bursts (GRBs) are fitted by connecting their event rates with cosmic star formation rates using power-law distributed delay times f (tau) proportional to tau(-1), where a broken-power-law luminosity function is assumed and some empirical observational selection effects are taken into account. As a result, the most-likely model parameters are constrained to be nu(1) = 0.91, nu(2) = 1.66 as power-law indices, with a break at L-b = 2.51 x 10(51) erg s(-1) for the luminosity function and tau(c) = 6.0 Gyr for a typical gravitatio...