  Corrections to scaling in the 3D Ising model are studied based on
non-perturbative analytical arguments and Monte Carlo (MC) simulation data for
different lattice sizes L. Analytical arguments show the existence of
corrections with the exponent (gamma-1)/nu (approximately 0.38), the leading
correction-to-scaling exponent being omega =< (gamma-1)/nu. A numerical
estimation of omega from the susceptibility data within 40 =< L =< 2048 yields
omega=0.25(33). It is consistent with the statement omega =< (gamma-1)/nu, as
well as with the value omega = 1/8 of the GFD theory. We reconsider the MC
estimation of omega from smaller lattice sizes to show that it does not lead to
conclusive results, since the obtained values of omega depend on the particular
method chosen. In particular, estimates ranging from omega =1.274(72) to
omega=0.18(37) are obtained by four different finite-size scaling methods,
using MC data for thermodynamic average quantities, as well as for partition
function zeros. We discuss the influence of omega on the estimation of
exponents eta and nu.
