Self-driving cars hold out the promise of being safer than manually driven cars. Yet they cannot be a 100 % safe. Collisions are sometimes unavoidable. So self-driving cars need to be programmed for how they should respond to scenarios where collisions are highly likely or unavoidable. The accident-scenarios self-driving cars might face have recently been likened to the key examples and dilemmas associated with the trolley problem. In this article, we critically examine this tempting analogy. We identify three important ways in which the ethics of accident-algorithms for self-driving cars and the philosophy of the trolley problem differ from each other. These concern: the basic decision-making situation faced by those who decide how self-driving cars should be programmed to deal with accidents; moral and legal responsibility; and decision-making in the face of risks and uncertainty. In discussing these three areas of disanalogy, we isolate and identify a number of basic issues and complexities that arise within the ethics of the programming of self-driving cars.