From The General Theory of Second Best, by R. G. Lipsey and Kelvin Lancaster, The Review of Economic Studies, Vol. 24, No. 1 (1956 - 1957), pp. 11-32
It is well known that the attainment of a Paretian optimum requires the simultaneous fulfillment of all the optimum conditions. The general theorem for the second best optimum states that if there is introduced into a general equilibrium system a constraint which prevents the attainment of one of the Paretian conditions, the other Paretian conditions, although still attainable, are, in general, no longer desirable. In other words, given that one of the Paretian optimum conditions cannot be fulfilled, then an optimum situation can be achieved only by departing from all the other Paretian conditions. The optimum situation finally attained may be termed a second best optimum because it is achieved subject to a constraint which, by definition, prevents the attainment of a Paretian optimum.Everyone who takes Econ 1 (or its equivalent) learns this; it doesn't seem to me that people remember it very well.