The decades of research in motion planning have resulted in numerous algorithms. Many of the most successful algorithms are randomized and can have widely differing run-times for the same problem instance from run to run. While this property is known to be undesirable from user's point of view, it has been largely ignored in past research. This paper introduces the large run-cost variance of randomized motion planners as a distinct issue to be addressed in future research. Run-cost variance is an important performance characteristic of an algorithm that should be studied together with the mean run-cost. As a positive example of possibilities for reducing the run-cost variance of a randomized motion planner, simple heuristic techniques are introduced and investigated empirically.