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Compact arc-shaped conformal dielectric resonator antennas (DRAs) loaded by metal plates and high-dielectric-constant (HiK) patches are investigated. Their miniaturizing principles are analyzed from different aspects. Closed-form expressions are derived to characterize the function of the conformal ground in size reduction. Difference between the conventional flat ground and conformal one is discussed. As to lateral metal loading, its influence on radiation patterns are utilized to acquire additional function. Next, to replace the metallic structure, HiK patches are used as perfect electric conductor (PEC) walls. Their working mechanisms are analyzed through the electromagnetic theory in layered media, and waveguide-based simulation methods. As validation, a dielectric-loaded arc DRA is proposed. By working like a PEC, the thin dielectric patch reduces the DRA size to one half. Similar characteristics are observed between the dielectric- and metal-loaded antennas. Finally, a bare DRA and a miniaturized one are fabricated and measured. This research expands the miniaturizing theory of conformal arc DRAs.