Inventory control for parts with infrequent demands is difficult since forecasting their demand is problematic. Traditional forecasting methods, such as moving average and single exponential smoothing, are known not to suffice since they do not cope well with periods with zero demands. Croston type methods and bootstrapping methods are more promising. We propose a new bootstrapping method, which we term empirical plus. The added value of this method lies in the fact that it explicitly takes into account that besides the demand, also the supply lead time is stochastic. We compare its performance with a number of methods from all three above-mentioned categories. Opposite to what is done in most comparative studies, we do not focus on performance metrics that are related directly to the forecasting results (e.g., mean squared error), but we focus on the resulting inventory control policy (achieved fill rate and holding costs). We use in our study large data sets from three companies, which we make publicly available. We find that our empirical plus method outperforms the other methods when the average inter-demand interval is large and the squared coefficient of variation of the demand size is small. This class of parts often consists of the expensive parts, for which forecasting is both difficult, because of the infrequent demands, and important, because of the price. The Syntetos Boylan approximation performs best on the other classes of parts. These findings may be used in practice to use the right forecasting method for each type of part, thus achieving more cost-effective spare parts inventory control.