Although the theory that creativity requires blind variation and selective retention (BVSR) is now more than a half-century old, only recently has BVSR theory undergone appreciable conceptual development, including formal three-parameter definitions of both creativity and sightedness. In this article, these new developments are for the first time extended to encompass sequential BVSR, that is, when ideas are generated and tested consecutively rather than simultaneously. Formulated in terms of creative problem solving, sequential BVSR is shown to have two forms: (a) "exploratory" in which the person decreases total ignorance and (b) "eliminatory" in which the person vets informed guesses. Only in the latter case does sightedness for both single potential solutions and the set of potential solutions necessarily increase with each generation-and-test trial. Exploratory BVSR is illustrated by Edison's search for a practical incandescent filament, whereas eliminatory BVSR is exemplified by Watson's discovery of the DNA base code. Hence, although epistemologically and psychologically distinct, both represent important forms of creative problem solving. (Contains 3 tables.)