This paper presents an efficient algorithm for the incremental construction of a minimal acyclic sequential transducer (ST) from a list of input and output strings. The algorithm generalizes a known method of constructing minimal finite-state automata (Daciuk, Mihov, Watson and Watson 2000). Unlike the algorithm published by Mihov and Maurel (2001), it does not require the input strings to be sorted in advance. The algorithm is illustrated by an application in a text-to-speech system.