During natural viewing, the oculomotor system interacts with depth information through a correlated, tightly related linkage between convergence, accommodation, and pupil miosis known as the near response. When natural viewing breaks down, such as when depth distortions and cue conflicts are introduced in a stereoscopic remote vision system (sRVS), the individual elements of the near response may decouple (e.g., vergence-accommodation, or VA, mismatch), limiting the comfort and usability of the sRVS. Alternatively, in certain circumstances the near response may become more tightly linked to potentially preserve image quality in the presence of significant distortion. In this experiment, we measured two elements of the near response (vergence posture and pupil size) of participants using an sRVS. We manipulated the degree of depth distortion by changing the viewing distance, creating a perceptual compression of the image space, and increasing the VA mismatch. We found a strong positive cross-correlation of vergence posture and pupil size in all participants in both conditions. The response was significantly stronger and quicker in the near viewing condition, which may represent a physiological response to maintain image quality and increase the depth of focus through pupil miosis.