  We continue the study, begun by the second author in math.AG/0701889, of
secant defective manifolds having "simple entry loci". We prove that such
manifolds are rational and describe them in terms of tangential projections.
Using also our results in math.AG/0701885, their classification is reduced to
the case of Fano manifolds of high index, whose Picard group is generated by
the hyperplane section class. Conjecturally, the former should be linear
sections of rational homogeneous manifolds. We also provide evidence that the
classification of linearly normal dual defective manifolds with Picard group
generated by the hyperplane section should follow along the same lines.
