This work describes the Edinburgh submission to the SIGMORPHON 2021 Shared Task 2 on unsupervised morphological paradigm clustering. Given raw text input, the task was to assign each token to a cluster with other tokens from the same paradigm. We use Adaptor Grammar segmentations combined with frequency-based heuristics to predict paradigm clusters. Our system achieved the highest average F1 score across 9 test languages, placing first out of 15 submissions.