This study investigated whether various kinds of preschool programs have differential cognitive effects on different kinds of children. Relevant literature was reviewed and data, generated in the first 2 years of the Head Start Planned Variations Study (PVS), were analyzed. The eight preschool programs associated with the PVS were considered. Children's characteristics used for analysis were initial ability, previous school experience, sex, age, socioeconomic status, ethnicity, and style of response to testing. Cognitive outcomes were assessed with the Preschool Inventory and Stanford-Binet. Several tentative conclusions were drawn. First, some children's characteristics interact more powerfully than others with characteristics of preschool models. Response style and previous schooling seemed the most important variables. Second, where interactions are consistent, they follow suggestive patterns. Educationally disadvantaged children seem to achieve more in highly directive programs than in less directive ones. Third, the interactions may be significant factors in preschool success or failure. Many educational approaches may be needed, to be delivered in a flexible classroom designed to accomodate all kinds of children. (DP)