  We propose an extension of the F-maximization principle to take into account
the effects of non-superconformality. Guided by a four-dimensional analog, we
formulate a modification of the free energy via the Lagrange multiplier
technique. We conjecture that the Lagrange multiplier plays the same role as
the coupling constant, at least at weak coupling. We check our proposal in many
examples with unitary, symplectic and orthogonal gauge groups.
