This paper was presented at a meeting of the Institute in London on 18 February 1981 with Dr J. F. Kemp in the Chair. Captain Alderton discusses a variety of criteria for assessing economic optimal speeds and shows how sensitive these optima are to such constraints as port time, voyage distance and bunker costs.The expression ‘optimum’ is frequently used very loosely and one often finds that the factor under consideration is only being optimized with reference to some, not all, of its dependent variables. A truly optimum speed for a ship can only be achieved by considering:(i) What speeds the ship can actually achieve, taking into account various mechanical constraints, the state of the hull (fouling), the draft and the effect of the weather.(ii) What speeds we would like the ship to achieve taking into account the costs, the profits and the pressure of schedules.