Unit selection algorithms are discussed to reduce delays in concatenative speech synthesis. Prompt synthesis response is very important, for example, in dialog systems. However, using a larger database for high-quality sounds, the time required for unit selection becomes longer. In this paper, beam search and DP search algorithms with a depth restriction in search trees are introduced in order to reduce delays in unit selection. In order to maintain the depth of the search tree, the root node is removed and a child node becomes the new root. In the process, all branches that do not pass through the new root are pruned. Therefore, the pruning may influence the result of the unit selection because many potential units can be removed from the search tree. The results of unit selection indicated that the depth-restricted beam search is superior to the depth-restricted DP search only when the depth limit is small.