  We make precise determinations of the leading scaling dimensions and operator
product expansion (OPE) coefficients in the 3d Ising, $O(2)$, and $O(3)$ models
from the conformal bootstrap with mixed correlators. We improve on previous
studies by scanning over possible relative values of the leading OPE
coefficients, which incorporates the physical information that there is only a
single operator at a given scaling dimension. The scaling dimensions and OPE
coefficients obtained for the 3d Ising model, $(\Delta_{\sigma},
\Delta_{\epsilon},\lambda_{\sigma\sigma\epsilon},
\lambda_{\epsilon\epsilon\epsilon}) = (0.5181489(10), 1.412625(10),
1.0518537(41), 1.532435(19))$, give the most precise determinations of these
quantities to date.
