  We consider seesaw type-I models including at least one (mostly-)sterile
neutrino with mass at the eV scale. Three distinct situations are found, where
the presence of light extra neutrinos is naturally justified by an
approximately conserved lepton number symmetry. To analyse these scenarios
consistently, it is crucial to employ an exact parametrisation of the full
mixing matrix. We provide additional exact results, including generalised
versions of the seesaw relation and of the Casas-Ibarra parametrisation, valid
for every scale of seesaw. We find that the existence of a light sterile
neutrino imposes an upper bound on the lightest neutrino mass. We further
assess the impact of light sterile states on short- and long-baseline neutrino
oscillation experiments, emphasise future detection prospects, and address CP
Violation in this framework via the analysis of CP asymmetries and construction
of weak basis invariants. The proposed models can accommodate enough
active-sterile mixing to play a role in the explanation of short-baseline
anomalies.
