[en] A new design has been developed for shaping pole tips to produce the radially increasing fields required for isochronous cyclotrons. The conventional solid hill poles are replaced by poles mounted over a small secondary gap which tapers radially from maximum at the magnet edge to zero near the center. Field measurements with a model magnet and calculations with the code TRIM show an increase in field at the edge of the magnet without the usual corresponding large increase in fringing, and a radial field shape more nearly field independent than for conventional hills. The flying hills have several advantages for variable energy multiparticle cyclotrons: (1) a large reduction in the power dissipated by isochronizing trim coils; (2) a more constant shape and magnitude flutter factor, eliminating flutter coils and increasing the operating range; and (3) a sharper fall-off of the fringe field, simplifying beam extraction