In this paper, we focus on two unnoticed problems in the seminal paper by Curtmola et al. First, we show that SSE-2 does not appropriately implement Curtmola et al.’s construction idea for dummy addition. We refine SSE-2’s (and its variants’) dummy-adding procedure to keep the number of dummies sufficiently many but as small as possible. We then show how to extend it to the dynamic setting while keeping the dummy-adding procedure work well and implement our scheme to show its practical efficiency. Second, we point out that the SSE-1 can cause a search error when a searched keyword is not contained in any document file stored at a server and show how to fix it.