Binary kernel discrimination (BKD) uses a training set of compounds, for which structural and qualitative activity data are available, to produce a model that can then be applied to the structures of other compounds in order to predict their likely activity. Experiments with the MDL Drug Data Report database show that the optimal value of the smoothing parameter, and hence the predictive power of BKD, is crucially dependent on the number of false positives in the training set. It is also shown that the best results for BKD are achieved using one particular optimization method for the determination of the smoothing parameter that lies at the heart of the method and using the Jaccard/Tanimoto coefficient in the kernel function that is used to compute the similarity between a test set molecule and the members of the training set.