Before revision:  Even worse, it is known that the "second best" mechanism-the mechanism that maximizes social welfare subject to the other constraints-has to be carefully tailored to the Bayesian priors and is extremely complex.
After revision:  Even worse, it is known that the "second best" mechanism-the mechanism that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the other constraints-has to be carefully tailored to the Bayesian priors and is extremely complex.