  The Hilbert scheme of projective 3-folds of codimension 3 or more that are
linear scrolls over the projective plane or over a smooth quadric surface or
that are quadric or cubic fibrations over the projective line is studied. All
known such threefolds of degree from 7 to 11 are shown to correspond to smooth
points of an irreducible component of their Hilbert scheme, whose dimension is
computed. A relationship with the locus of good determinantal subschemes is
investigated
