When applying the 2-opt heuristic to the travelling salesman problem, selecting the best improvement at each iteration gives worse results on average than selecting the first improvement, if the initial solution is chosen at random. However, starting with solutions of ‘greedy’ or ‘nearest neighbor’ constructive heuristics, the best improvement is better and faster on average. Reasons for this behavior are investigated. It appears to be better to use exchanges introducing into the solution a very small edge and a fairly large one, which can easily be removed later, than two small ones which are much harder to remove.