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The generalized Busemann-Petty problem asks whether the origin-symmetric convex bodies in Rn with a larger volume of all i-dimensional sections necessarily have a larger volume. As proved by Bourgain and Zhang, the answer to this question is negative if i ＞ 3. The problem is still open for i = 2, 3. In this article we prove two specific affirmative answers to the generalized Busemann-Petty problem if the body with a smaller i-dimensional volume belongs to given classes. Our results generalize Zhang's specific affirmative answer to the generalized Busemann-Petty problem.