  We study the off-equilibrium relaxational dynamics at criticality in the
three-dimensional Blume-Capel model whose static critical behaviour belongs to
the 3d-Ising universality class. Using "improved" Hamiltonian (the leading
corrections to scaling have vanishing amplitude) we perform Monte Carlo
simulations of the relaxational dynamics after a quench from $T=\infty$ to
$T_c$. Analysing the off-equilibrium dynamics at $T_c$ we obtain an estimate of
the dynamical critical exponent $z=2.020(8)$ that is perfectly consistent with
the Field Theory predictions.
