I investigate use of the simulated annealing heuristic to seek phylogenetic trees judged optimal according to the principle of parsimony. I begin by looking into the central data structure in phylogenetic research, the tree. I discuss why it is usually necessary to employ a heuristic, rather than an exact method, when seeking parsimonious trees. I summarise different heuristic approaches. I explain how to use the program LVB, written to use simulated annealing in the search for parsimonious trees. I use LVB, with different combinations of values for parameters controlling the annealing search, to re-analyse two DNA sequence data matrices, one of 50 objects and one of 365 objects. Equations to estimate suitable control parameters, on the basis of desired run time and quality of result, are fitted to data obtained by these analyses. Future directions of research are discussed.