  When the Standard Model is interpreted as the renormalizable sector of a
low-energy effective theory, the effects of new physics are encoded into a set
of higher dimensional operators. These operators potentially deform the shapes
of Standard Model differential distributions of final states observable at
colliders. We describe a simple and systematic method to obtain optimal
estimations of these deformations when using numerical tools, like Monte Carlo
simulations. A crucial aspect of this method is minimization of the estimation
uncertainty: we demonstrate how the operator coefficients have to be set in the
simulations in order to get optimal results. The uncertainty on the
interference term turns out to be the most difficult to control and grows very
quickly when the interference is suppressed. We exemplify our method by
computing the deformations induced by the ${\cal O}_{3W}$ operator in $W^+W^-$
production at the LHC, and by deriving a bound on ${\cal O}_{3W}$ using $8$ TeV
CMS data.
