  We study the special point in the phase diagram of a semi-infinite system,
where the bulk transition is in the three-dimensional Ising universality class.
To this end we perform a finite size scaling study of the improved Blume-Capel
model on the simple cubic lattice with two different types of surface
interactions. In order to check for the effect of leading bulk corrections we
have also simulated the spin-1/2 Ising model on the simple cubic lattice. We
have accurately estimated the surface enhancement coupling at the special point
of these models. We find $y_{t_s}=0.718(2)$ and $y_{h_s}=1.6465(6)$ for the
surface renormalization group exponents of the special transitions. These
results are compared with previous ones obtained by using field theoretic
methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore we
study the behaviour of the surface transition near the special point and
finally we discuss films with special boundary conditions at one surface and
fixed ones at the other.
