Pneumatic tires for aircraft service having a belt package with shoulder reinforcement. The tire includes a belt reinforcing structure or belt package having multiple cut belts, multiple spiral wound belt layers positioned radially between the cut belts and the tread, and multiple spiral wound shoulder layers proximate the shoulder. The spiral wound belt layers and the spiral wound shoulder layers are formed by a continuous cord-reinforced strip having a strip width. The spiral wound belt layers are characterized by a first winding pitch of approximately one strip width per revolution and the spiral wound shoulder layers are characterized by a second winding pitch of less than one strip width per revolution. Alternatively, the spiral wound shoulder layers may be formed with a tiered arrangement by shifting the starting location for successive spiral wound belt layers laterally so that the side edges are not coincident.