This paper presents high-resolution (0.6") spectropolarimetric observations of very quiet solar regions. We make determinations of the magnetic flux density, intrinsic field strength, and magnetic filling factor in these regions. Our results confirm other previous works in that most of the internetwork flux is in the form of intrinsically strong fields. However, in contrast to other recent observations, we do not find a significant increase in the amount of unsigned magnetic flux relative to that measured at an angular resolution of 1", nor do we find that most internetwork lanes are populated by strong flux. We discuss possible causes for this disparity. The lack of additional flux with increased resolution may be used to set constrains on the typical spatial scales at which mixed polarities occur (smaller than ~=0.6").