Zero-resource word segmentation and clustering systems aim to tokenise speech into word-like units without access to text labels. Despite progress, the induced lexicons are still far from perfect. In an idealised setting with gold word boundaries, we ask whether performance is limited by the representation of word segments, or by the clustering methods that group them into word-like types. We combine a range of self-supervised speech features (continuous/discrete, frame/word-level) with different clustering methods (K-means, hierarchical, graph-based) on English and Mandarin data. The best system uses graph clustering with dynamic time warping on continuous features. Faster alternatives use graph clustering with cosine distance on averaged continuous features or edit distance on discrete unit sequences. Through controlled experiments that isolate either the representations or the clustering method, we demonstrate that representation variability across segments of the same word type -- rather than clustering -- is the primary factor limiting performance.