In test-time reasoning, pairing a weak local generator with a strong but expensive teacher makes deployment cost hinge on when additional teacher computation is worthwhile. We propose Cascade-SC, a containment-gated cascade that accepts the teacher’s independently solved answer when it matches the generator’s candidate set and draws additional teacher samples otherwise. The cross-model gate fires roughly 5× less often than within-model unanimity, concentrating teacher compute on harder cases. Across GSM8K, MATH500, and AIME-2024, Cascade-SC improves over self-consistency by 11–37%. On GSM8K, it matches ModelSwitch within 0.46% at roughly one-third the teacher-inference cost and beats matched-compute Teacher-only SC by 1.71%. On low-recall AIME-2024, it reaches 40.00% versus the candidate-restricted Oracle@8 ceiling of 11.11%. It also outperforms trained 7B process-reward rerankers by 4–11% without verifier training. Self-consistency and Teacher-greedy arise as special cases, while a teacher-only versus union-vote ablation shows that aggregation is a separate design choice. Source codes are available at https://github.com/SUGAR-NLP/Cascade-SC.