Visual perception is largely supported by tiny fixational eye movements (FEMs), the control of which is a mystery. Understanding eye movement control has been impeded by researchers recording one eye, assuming the other behaves symmetrically as if “yoked” (Hering’s Law). However, recent work revealed asynchronous smooth eye movements during vergence, challenged Hering’s Law, suggesting FEMs might also be decoupled. We assessed FEMs of both eyes during binocular and monocular viewing. During binocular viewing, eye movement variability (BCEA) was larger in one eye, implying the eyes were independently controlled. During monocular viewing, covered eyes’ BCEAs were larger than viewing ones. Eyes with larger BCEAs drifted faster, suggesting poorer eye control. In contrast, microsaccades were always binocular, yet larger in viewing eyes with larger BCEAs, indicating independent control improved their drift correction. Our results support independent control of smooth eye movements and elucidate the genesis of ocular misalignment relevant to strabismus intervention.