Low energy effects of generic extensions of the Standard Model can be comprehensively parametrized in terms of higher dimensional effective operators. After the success of all the recent precission tests on the Standard Model, we argue that any sensible description of these extensions at the Z-scale must be stable under higher order quantum corrections. The imposition of SU(2)L×U(1)Y gauge invariance seems to be the simplest and most natural way to fulfill this requirement. With this assumption, all the possible deviations from the standard triple gauge boson vertices can be consistently parametrized in terms of a finite set of gauge invariant operators. We deal here with those operators that do not give any tree level effect on present experimental observables and constrain them by computing their effects at the one-loop level. We conclude that for a light Higgs boson, the direct measurement at LEP200 can improve present bounds on these 'blind directions', while for a heavy Higgs it is most unlikely to provide any new information.