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This paper considers a popular class of recommender systems that are based on Collaborative Filtering (CF) and proposes a novel technique for diversifying the recommendations that they give to users. Items are clustered based on a unique notion of priority-medoids that provides a natural balance between the need to present highly ranked items vs. highly diverse ones. Our solution estimates items diversity by comparing the rankings that different users gave to the items, thereby enabling diversification even in common scenarios where no semantic information on the items is available. It also provides a natural zoom-in mechanism to focus on items (clusters) of interest and recommending diversified similar items. We present DiRec a plug-in that implements the above concepts and allows CF Recommender systems to diversify their recommendations. We illustrate the operation of DiRec in the context of a movie recommendation system and present a thorough experimental study that demonstrates the effectiveness of our recommendation diversification technique and its superiority over previous solutions.