  We study the cosmological constraints on active-sterile neutrino oscillations
nu_e <-> nu_s for the case when nu_s is partially filled initially, i.e. 0 <
delta N_s < 1. We provide numerical analysis of the cosmological production of
He-4, in the presence of nu_e <-> nu_s oscillations, effective after neutrino
decoupling, accounting for all known oscillations effects on cosmological
nucleosynthesis. Cosmological constraints on oscillation parameters
corresponding to higher than 5% He-4 overproduction and different non-zero
initial populations of the sterile state delta N_s < 1 are calculated. These
generalized cosmological constraints corresponding to delta N_s > 0 are relaxed
in comparison with the delta N_s = 0 case and the relaxation is proportional to
delta N_s.
