Compact radiators with circular polarization are important components of modern mobile communication systems. Their design is a challenging process which requires maintaining simultaneous control over several performance figures but also the structure size. In this work, a novel design framework for multi-stage constrained miniaturization of antennas with circular polarization is presented. The method involves se- quential optimization of the radiator in respect of selected performance figures and, eventually, the size. Optimizations are performed with iteratively increased number of design constraints. Numerical efficiency of the method is ensured using a fast local-search algorithm embedded in a trust-region framework. The proposed design framework is demonstrated using a compact planar radiator with circular polarization. The optimized antenna is characterized by a small size of 271 mm2 with 37% and 47% bandwidths in respect of 10 dB return loss and 3 dB axial ratio, respectively. The structure is benchmarked against the state-of-the-art circular polarization antennas. Numerical results are confirmed by measurements of the fabricated antenna prototype.