The paper presents a case study of a secondary school in Israel and its efforts at attending to students' needs without resorting to tracking and ability grouping. It explores an organisational process the school has established, called "Opening triads", which involves periodical regrouping of three classrooms of students of the same age and same subject matter into three new groups. The findings suggest that ability grouping is difficult to eliminate, but there are alternatives that may reduce its social and emotional harmful effect. Ability grouping can be avoided altogether through other, more equalitarian forms of regrouping students. (Contains 2 tables.)