We define a method for the analysis of the integrated spectra of extragalactic globular clusters that provides more reliable measures of the age, metallicity and α-element abundance ratio than have so far been achieved. The method involves the simultaneous fitting of up to 25 Lick indices in a χ2 fitting technique that maximizes the use of the available data. Here we compare three sets of single stellar population (SSP) models of Lick indices to the high signal-to-noise, integrated spectra of 20 Galactic globular clusters. The ages, [Fe/H] and α-element abundance ratios derived from the SSP models are compared with the results of resolved stellar population studies from the literature. We find good consistency with the published values, with an agreement of better than 0.1 dex in all three derived parameters. The technique allows the identification of abundance ratio anomalies, such as the known nitrogen overabundance in Galactic globular clusters, and the presence of anomalous horizontal branch morphologies. It also minimizes the impact on the derived parameters of imperfect calibration to the Lick system, and reduction errors in general. The method defined in this paper is therefore robust with respect to many of the difficulties that plague the application of SSP models in general. Consequently, it is well suited to the study of extragalactic globular cluster systems.