The collision between the dredger Bowbelle and the pleasure cruiser Marchioness on the Thames in August 1989 in the vicinity of the centre of London has drawn attention to the need for river mariners to keep a frequent look-out astern as well as ahead. This paper describes calculations of the minimum frequency at which observations astern are required in order to allow sufficient time for a ship about to be overtaken by a faster vessel to be able to take adequate avoidance action should the overtaking craft fail to keep clear.