  We classify all non-extendable 3-sequences of half-fibers on Enriques
surfaces. If the characteristic is different from 2, we prove in particular
that every Enriques surface admits a 4-sequence, which implies that every
Enriques surface is the minimal desingularization of an Enriques sextic, and
that every Enriques surface is birational to a Castelnuovo quintic.
