  We perform high-statistics Monte Carlo simulations of three-dimensional Ising
spin-glass models on cubic lattices of size L: the +- J (Edwards-Anderson)
Ising model for two values of the disorder parameter p, p=0.5 and p=0.7 (up to
L=28 and L=20, respectively), and the bond-diluted bimodal model for
bond-occupation probability p_b = 0.45 (up to L=16). The finite-size behavior
of the quartic cumulants at the critical point allows us to check very
accurately that these models belong to the same universality class. Moreover,
it allows us to estimate the scaling-correction exponent \omega related to the
leading irrelevant operator: \omega=1.0(1). Shorter Monte Carlo simulations of
the bond-diluted bimodal models at p_b=0.7 and p_b=0.35 (up to L=10) and of the
Ising spin-glass model with Gaussian bond distribution (up to L=8) also support
the existence of a unique Ising spin-glass universality class. A careful
finite-size analysis of the Monte Carlo data which takes into account the
analytic and the nonanalytic corrections to scaling allows us to obtain precise
and reliable estimates of the critical exponents \nu and \eta: we obtain
\nu=2.45(15) and \eta=-0.375(10).
