FLAVERS is a finite-state verification approach that allows an analyst to incrementally add constraints to improve the precision of the model of the system being analyzed. Except for trivial systems, however, it is impractical to compute which constraints should be selected to produce precise results for the least cost. Thus, constraint selection has been a manual task, guided by the intuition of the analyst. In this paper, we investigate several heuristics for selecting task automaton constraints, a kind of constraint that tends to reduce infeasible task interactions. We describe an experiment showing that one of these heuristics is extremely effective at improving the precision of the analysis results without significantly degrading performance.