  We study the syzygetic structure of projections of del Pezzo surfaces in
order to construct singular Calabi-Yau threefolds. By smoothing those
threefolds, we obtain new examples of Calabi-Yau threefolds with Picard group
of rank 1. We also give an example of type II primitive contraction whose
exceptional divisor is the blow-up of the projective plane at a point.
