The primary contribution of this paper is a secure method for doing top-k selection from vertically partitioned data. This has particular relevance to privacy-sensitive searches, and meshes well with privacy policies such as k-anonymity. We have demonstrated how secure primitives from the literature can be composed with efficient query processing algorithms, with the result having provable security properties. The paper also shows a trade-off between efficiency and disclosure. It is worth exploring whether one could have a suite of algorithms to optimize these tradeoffs, e.g., algorithms that guarantee k-anonymity with efficiency based on the choice of k rather than the guarantees of secure multiparty computation.