In high energy solar astrophysics, imaging hard X-rays by direct focusing offers higher dynamic range and greater sensitivity compared to past techniques that used indirect imaging. The Focusing Optics X-ray Solar Imager (FOXSI) is a sounding rocket payload that uses seven sets of nested Wolter-I figured mirrors together with seven high-sensitivity semiconductor detectors to observe the Sun in hard X-rays through direct focusing. The FOXSI rocket has successfully flown twice and is funded to fly a third time in summer 2018. The Wolter-I geometry consists of two consecutive mirrors, one paraboloid and one hyperboloid, that reflect photons at grazing angles. Correctly focused X-rays reflect once per mirror segment. For extended sources, like the Sun, off-axis photons at certain incident angles can reflect on only one mirror and still reach the focal plane, generating a background pattern of singly reflected rays (i.e., ghost rays) that can limit the sensitivity of the observation to faint, focused sources. Understanding and mitigating the impact of the singly reflected rays on the FOXSI optical modules will maximize the instruments’ sensitivity to background-limited sources. We present an analysis of the FOXSI singly reflected rays based on ray-tracing simulations and laboratory measurements, as well as the effectiveness of different physical strategies to reduce them.