Person re-identification (re-ID) is a valuable tool for multi-camera tracking of persons. Up till now, research on person re-ID has mainly focused on the closed-set case, where a given query is assumed to always have a correct match in the gallery set, which does not hold for practical scenarios. In this study, we explore the open-set person re-ID problem with queries not always included in the gallery set. First, we convert the popular closed-set person re-ID datasets into the open-set scenario. Second, we compare the performances of six state-of-the-art closed-set person re-ID methods under open-set conditions. Third, we investigate the impact of a simple and fast statistics-driven gallery refinement approach on the open-set person re-ID performance. Extensive experimental evaluations show that, gallery refinement increases the performance of existing methods in the low false-accept rate (FAR) region, while simultaneously reducing the computational demands of retrieval. Results show an average detection and identification rate (DIR) increase of 7.91% and 3.31% on the DukeMTMC-reID and Market1501 datasets, respectively, for an FAR of 1%.