  We present a Monte Carlo study of the one-component $\phi^4$ model on the
cubic lattice in three dimensions. Leading order scaling corrections are
studied using the finite size scaling method. We compute the corrections to
scaling exponent $\omega$ with high precision. We determine the value of the
coupling $\lambda$ at which leading order corrections to scaling vanish. Using
this result we obtain estimates for critical exponents that are more precise
than those obtained with field theoretic methods.
