Skeletal reaction models for n-butane and iso-butane combustion are derived from a detailed chemistry model through directed relation graph (DRG) and DRG-aided sensitivity analysis (DRGASA) methods. It is shown that the accuracy of the reduced models can be improved by optimization through the method of uncertainty minimization by polynomial chaos expansion (MUM-PCE). The dependence of model uncertainty on the model size is also investigated by exploring skeletal models containing different number of species. It is shown that the dependence of model uncertainty is subject to the completeness of the model. In principle, for a specific simulation the uncertainty of a complete model, which includes all reactions important to its prediction, is convergent with respect to the model size, while the uncertainty calculated with an incomplete model may display unpredictable correlation with the model size. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.