During visual fixation, we constantly move our eyes. These microscopic eye movements are composed of tremor, drift, and microsaccades. Early studies concluded that microsaccades, like larger saccades, are binocular and conjugate, as expected from Hering's law of equal innervation. Here, we document the existence of monocular microsaccades during both fixation and a discrimination task, reporting the location of the gap in a foveal, low-contrast letter C. Monocular microsaccades differ in frequency, amplitude, and peak velocity from binocular microsaccades. Our analyses show that these differences are robust to different velocity and duration criteria that have been used previously to identify microsaccades. Also, the frequency of monocular microsaccades differs systematically according to the task: monocular microsaccades occur more frequently during fixation than discrimination, the opposite of their binocular equivalents. However, during discrimination, monocular microsaccades occur more often around the discrimination threshold, particularly for each subject's dominant eye and in case of successful discrimination. We suggest that monocular microsaccades play a functional role in the production of fine corrections of eye position and vergence during demanding visual tasks.