Itemset mining typically results in large amounts of redundant itemsets. Several approaches such as closed itemsets, non-derivable itemsets and generators have been suggested for losslessly reducing the amount of itemsets. We propose a new pruning method based on combining techniques for closed and non-derivable itemsets that allows further reductions of itemsets. This reduction is done without loss of information, that is, the complete collection of frequent itemsets can still be derived from the collection of closed non-derivable itemsets. The number of closed non-derivable itemsets is bound both by the number of closed and the number of non-derivable itemsets, and never exceeds the smaller of these. Our experiments show that the reduction is significant in some datasets.