  We present a Monte Carlo study of the two-component $\phi^4$ model on the
simple cubic lattice in three dimensions. By suitable tuning of the coupling
constant $\lambda$ we eliminate leading order corrections to scaling. High
statistics simulations using finite size scaling techniques yield
$\nu=0.6723(3)[8]$ and $\eta=0.0381(2)[2]$, where the statistical and
systematical errors are given in the first and second bracket, respectively.
These results are more precise than any previous theoretical estimate of the
critical exponents for the 3D XY universality class.
