This paper considers the optimization of a class of joint source-channel codes described by finitestate encoders (FSEs) generating variable-length codes. It focuses on FSEs associated to joint-source channel integer arithmetic codes, which are uniquely decodable codes by design. An efficient method for computing the free distance of such codes using Dijkstra's algorithm is proposed. To facilitate the search for codes with good distance properties, FSEs are organized within a tree structure which allows the use of efficient branch-and-prune techniques avoiding a search of the whole tree.