It is argued that aptitude and achievement tests designed for much older students are invaluable for finding extremely high ability at younger ages, particularly in mathematical and verbal reasoning. Results of the first two years of the Study of Mathematically and Scientifically Precocious Youth (SMSPY) are examined to show that considerable educational acceleration is not only feasible but also desirable for those young people who are eager to move ahead. Skipping school grades, taking college courses part-time, studying in special courses, and entering college early are proposed. These are simple to carry out. inexpensive, and supplemental to regular school practices. The SMSPY staff does not advocate the usual in-grade, non-accelerative "enrichment" procedures often recommended for intellectually gifted children. The approach in this paper is via cases and references to numerous SMSPY studies. It is meant to be an heuristic overview of the main assumptions and findings. (Author)