We propose a new class of compact integrated optical circulators providing a large isolation level while maintaining a straightforward technological feasibility. Their layout is based on a nonreciprocal radial Bragg cavity composed of concentric magneto-optical rings. The circulator ports are standard rib waveguides, butt-coupled to the cavity by cutting through its outer rings. The device is specifically designed for operation in a uniform external magnetic field. Using a coupled-mode description of the complete cavity/waveguide-port system, we explore the rich behaviour of cavity circulators in presence of varying levels of direct port-to-port coupling. We demonstrate numerically a strongly miniaturized two-dimensional cavity circulator, with a total footprint of less than (10λ)2, achieving a 20-dB isolation level at telecom frequencies over a bandwidth of 130 GHz. The device is found to be very tolerant with respect to fabrication imperfections. We finish with an outlook on three-dimensional versions of the proposed nonreciprocal cavities.