Surface complexation models (SCMs) have previously been shown to be capable of predicting metal ion sorption behavior onto mineral surfaces. Application of SCMs, however, requires a self-consistent approach for determining model parameter values. In this paper, titration data for alpha-Al2O3 and metal ion sorption data for Co(II) are used to determine the metal ion sorption parameters for the triple-layer model (TLM) version of the SCM, This was accomplished by calibrating the TLM parameters to a moderate-coverage (0.1%) data set and then using these values to predict data over a wide range of surface coverages (0.05 to 10%), pH(5 to 9), and ionic strength (0.001 to 0.1 M as NaNO3). The results of the analysis showed that a range of TLM parameter values could fit the calibration data set equally well. However, when metal ion sorption data covering a range of ionic strength and surface coverages were considered, an optimal set of TLM parameter values could be identified. For high surface coverage data (>10%), the model was shown to underpredict the data, presumably due to the formation of multinuclear species. In order to extend the model predictions range to high surface coverage, polymer or surface precipitation TLM reactions are needed.