The size reduction for wire antennas using lumped loading inductors is well known, but introduces significant degradation in efficiency and bandwidth. One of the alternative approaches to solve the problem is the increase of wire length for a fixed height. Various techniques have been investigated to introduce longer wire length, but this paper concentrates on helical windings with continuously varying radii. The continuously varying radii are represented using radial basis functions, which give maximized shape controllability with a minimal number of defining parameters. These parameters that define the shape of the helix are optimized with respect to both bandwidth and efficiency, and matching networks are included in the optimization. The results are obtained from an automated simulation tool (MATNEC) equipped with evolutionary optimizers. Using the proposed strategy, a performance improvement is predicted for an optimized helical winding structure with continuously varying radii.