It has been widely believed that deletions followed by insertions caused the internal path length of binary trees to be reduced on average. Recent empirical results obtained by Eppinger have cast doubt upon this assumption. This thesis adds to the empirical evidence through additional simulations, and investigates some plausible explanations. A few hypotheses are formed and simulations performed to test them. In addition, a brief exploration is made of a special case in which the number of available elements is the same as the number of nodes in the tree.