The concurrent logic languages, of which Parlog is one, have been promoted as a new generation of software languages specifically designed for parallel programming. This paper investigates their apphcation to a search problem commonly used as an illustration of artificial intelligence techniques, the 8-puzzle. It notes that programs written in the concurrent logic languages which do not pay attention to the parallehsm can fall into two possible traps: either there is little real parallelism in them due to data dependencies, or there is too much parallelism and any practical architecture will be overwhelmed. A solution which controls the parallehsm using user-defined priorities is proposed. This solution has the advantage of being architecture-independent.