Participants made decisions between two road improvements to increase mean speed. Time saved when speed increased from a higher driving speed was overestimated in relation to time saved from increases from lower speeds. In Study 2, participants matched pairs of speed increases so that they would give the same time saving and repeated the bias. The increase in risk of an accident with person injury was underestimated and the increase in risk of a fatal accident grossly underestimated when speed increased. The increase of stopping distance when speed increased was systematically underestimated. In Study 3, the tasks and results of Study 2 were repeated with engineering students. When forming opinions about speed limits and traffic planning, drivers, the public, politicians and others who do not collect the proper facts are liable to the same biases as those demonstrated in the present study. Copyright © 2008 John Wiley & Sons, Ltd.