A two-step approach to sensitivity analysis of model output in large computational models is proposed. A preliminary screening exercise is suggested in order to identify the subset of the most potentially explanatory factors. Afterwards, a quantitative method is recommended on the subset of preselected inputs. The advantage of the proposed procedure is that, very often, among a large number of input factors, only a few have a significant effect on the model output. The approach provides quantitative sensitivity measures while controlling the computational cost of the experiment. The procedure has been tested on a recent version of a chemical kinetics model of the tropospheric oxidation pathways of dimethylsulphide, including 68 uncertain factors.