The omnidirectional radiation scheme has been widely applied to thermal emitters for radiative cooling. We quantitatively illustrate that significant net radiative absorption at high zenith angles limits the performance of such isotropic emitters, and demonstrate that simply cutting off components corresponding to high angles can substantially improve the cooling performance of commonly used isotropic emitter designs. We also present an expression for the ideal directional spectral emissivity at conditions below ambient temperature. As our approach can be applied to coolers with arbitrary surfaces, our results may serve as a basic guideline for designing practical systems with various surfaces, such as rooftops or façades of modern buildings with complicated geometries.