We discuss electroweak precision constraints on dimension-6 operators in the effective theory beyond the standard model. We identify the combinations of these operators that are constrained by the pole observables (the W and Z masses and on-shell decays) and by the W boson pair production. To this end, we define a set of effective couplings of W and Z bosons to fermions and to itself, which capture the effects of new physics corrections. This formalism clarifies which operators are constrained by which observable, independently of the adopted basis of operators. We obtain numerical constraints on the coefficients of dimension-6 operator in a form that can be easily adapted to any particular basis of operators, or any particular model with new heavy particles.