Three different maps of the quiet Sun, observed with the Advanced Stokes Polarimeter (ASP) and the Diffraction-Limited Stokes Polarimeter (DLSP), show evidence of strong (~=1700 G) and weak (<500 G) fields coexisting within the resolution element at both network and internetwork locations. The angular resolution of the observations is of 1" (ASP) and 0.6" (DLSP). Even at the higher DLSP resolution, a significant fraction of the network magnetic patches harbor a mixture of strong and weak fields. Internetwork elements that exhibit kG fields when analyzed with a single-component atmosphere are also shown to harbor considerable amounts of weak fields. Only those patches for which a single-component analysis yields weak fields do not show this mixture of field strengths. Finally, there is a larger fractional area of weak fields in the convective upflows than in the downflows.