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We analyze an optical atomic clock using two-photon 5S1/2-4DJ transitions in rubidium. Four one- and two-color excitation schemes to probe the 4D3/2 and 4D5/2 fine-structure states are considered in detail. We compare key characteristics of Rb 4DJ and 5D5/2 two-photon clocks. The 4DJ clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the 10−13 τ (s)-level, with integration time τ in seconds, and a relative accuracy of ∼10−13/sqrt(t(s)). We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb 4DJ-states.