  We study the numerical bounds obtained using a conformal-bootstrap method -
advocated in ref. [1] but never implemented so far - where different points in
the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast
to the most used method based on derivatives evaluated at the symmetric point
$z=\bar z =1/2$, we can consistently "integrate out" higher-dimensional
operators and get a reduced simpler, and faster to solve, set of bootstrap
equations. We test this "effective" bootstrap by studying the 3D Ising and
$O(n)$ vector models and bounds on generic 4D CFTs, for which extensive results
are already available in the literature. We also determine the scaling
dimensions of certain scalar operators in the $O(n)$ vector models, with
$n=2,3,4$, which have not yet been computed using bootstrap techniques.
