Combining predictions made by multiple different prediction systems, including: obtaining a new input sample; obtaining a combiner which comprises optimal selection values that are configured to maximize a predefined performance measure; automatically applying multiple different prediction systems to the new input sample, to generate predictions; and automatically selectively combining the generated predictions based on the optimal selection values, to generate a combined prediction whose predefined performance measure is improved compared to individual usage of each of the prediction systems. The selective combination includes splitting the generated predictions into an intersection subset, fully-disjoint subsets, and optionally one or more partially-disjoint subsets; selecting predictions, from the subsets, at a ratio corresponding to the optimal selection values associated with the subsets, and modifying the subsets to remove all non-selected predictions; and merging all predictions in the modified subsets, to produce the combined prediction.