This article reviews the literature and practice (especially in New Mexico) concerning reading instruction of gifted children. It considers early or "precocious" reading, instruction in the early grades, and identification of the gifted in New Mexico. Reading teachers in New Mexico are urged to be aware of specific conflicts in the area of gifted identification and gifted instruction. The seven intelligences identified by H. Gardner are listed. The appropriateness of traditional basal reading programs for this population is questioned. A variety of literacy activities are encouraged, including guest speakers in the classroom, tie-ins of books with television or movies, student creative writing, investigatory activities, and activities which develop higher order thinking skills. (Contains 14 references.) (DB)