We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time allocated for review just-in-time, on-demand, and in-context. Students thereby complete Calculus III within two semesters of entering college rather than three. In a pilot study, comparative statistical analysis of student responses to multiple-choice questions suggested an equal or better performance is obtained with the new approach compared with the existing approach.