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This paper examines algorithmic aspects of searching for approximate functional dependencies in a database relation. The goal is to avoid exploration of large parts of the space of potential rules. This is accomplished by leveraging found rules to make finding other rules more efficient. The overall strategy is an attribute-at-a-time iteration which uses local breadth first searches on lattices that increase in width and height in each iteration. The resulting algorithm provides many opportunities to apply heuristics to tune the search for particular data-sets and/or search objectives. The search can be tuned at both the global iteration level and the local search level. A number of heuristics are developed and compared experimentally.