  We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model
on the three-dimensional simple cubic lattice with nearest neighbour
interactions. For this purpose, we use Monte Carlo simulations in connection
with a finite size scaling method. We find that there exists a finite value of
the coupling lambda^*, for both values of N, where leading corrections to
scaling vanish. As a first application, we compute the critical exponents
nu=0.710(2) and eta=0.0380(10) for N=3 and nu=0.749(2) and eta=0.0365(10) for
N=4.
