Abstract A recurring problem in cognitive science involves fitting a labelled tree structure to raw data. My APRIL parser analyses natural-language grammar by optimizing a labelled tree over an input string using the stochastic optimization technique of simulated annealing. Stochastic optimization is inherently processing-intensive, so it is desirable to speed the process up by exploiting the power of parallel computing; but the task of optimizing a tree structure does not at first sight lend itself to being shared between multiple processors. I define an algorithm which allows this to be done at the cost of requiring individual processors to operate with imperfect knowledge of the current solution; and I describe results of an implementation of this algorithm which suggest that the cost may be worth paying.