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This article outlines a research strategy for investigating, in a laboratory setting, the acquisition and the "limits" of a cognitive skill. Expert digit memory is used as an illustration. Two participants with initial average digit- and word-span memory were trained to memorize and reproduce strings of 80 to 90 digits presented at 10- to 1-sec rates. The instruction and training program, based on a theory of skilled memory, focused on three components: (a) acquisition of a mnemonic system (i.e., recoding digits into historical dates or concrete nouns), (b) use of a long-term memory retrieval structure (i.e., instruction in the Method of Loci), and (c) improvement in processing speed. After 86 experimental sessions, one participant recalled 90 random digits presented at a 1-sec rate. The digits were, however, constrained to be compatible with the participant's historical knowledge. The second participant recalled 80 random digits presented at a 5-sec rate after 70 sessions. Speed of encoding and retrieval processing was the only component that required extensive practice for skilled digit-memory acquisition.