  We study the Sivers effect in the transverse single spin asymmetries (SSA)
for pion and kaon production in semi-inclusive deep inelastic scattering
(SIDIS) processes. We perform a fit of A^sin(phi_h-phi_S)_UT which, by
including recent high statistics experimental data for pion and kaon production
from HERMES and COMPASS Collaborations, allows a new determination of the
Sivers distribution functions for quarks and antiquarks with u, d and s
flavours. Estimates for forthcoming SIDIS experiments at COMPASS and JLab are
given.
