Projective 7-folds with positive defect

New simple proofs are given for the classification theorems of projective k-folds X (k \leq 6) with defect \delta > 0 and those whith \delta = 1 and K_X \otimes O_X(5) spanned are classified. The section of th 10-dimensional spinor variety of P^{15} by three general hyperplanes and Grassmann fibrations over a smooth curve belong to this last class.