Observations of solar flares partially occulted by the solar limb provide diagnostics of coronal hard X-ray (HXR) emissions in the absence of generally much brighter emissions from footpoints of flare loops. In this paper, a statistical survey of 55 partially occulted flares observed by the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) is presented, revealing the existence of two different components of coronal HXR emissions. Below ~15 keV thermal HXR emission with a gradual time profile is generally dominant, while at higher energies an additional component is seen in 50 out of 55 events. This additional component shows faster time variations in the order of tens of seconds and is most prominent during the rise of the thermal emission. A comparison of the centroid positions of these two emissions shows that they are most often cospatial within ~2000 km, although for a few events clear separations are observed as well. The spectra of the high-energy component show a rather steep (soft) power law with indices mostly between ~4 and ~6. Thin target emission in the corona from flare-accelerated electrons is discussed as a possible origin of the fast time variation component.