The design and interpretation of surface hybridization assays is complicated by poorly understood aspects of the interfacial environment that cause both kinetic and thermodynamic behaviors to deviate from those in solution. The origins of these differences lie in the additional interactions experienced by hybridizing strands at the surface. In this report, an analysis of surface hybridization equilibria is provided for end-tethered, single-stranded oligonucleotide "probes" hybridizing with similarly sized, single-stranded solution "target" molecules. Theoretical models by Vainrub and Pettitt (Phys. Rev. E 2002, 66, 041905) and by Halperin, Buhot, and Zhulina (Biophys. J. 2004, 86, 718), and an "extended" model that in addition includes a solution-like salt dependence of probe-target dimerization, are compared to experiments as a function of salt concentration and probe coverage. Good agreement with experiment is observed when the DNA volume fraction at the surface remains below similar to 0.25. None of the models, however, can account for strong suppression of hybridization when the volume fraction of DNA approaches 0.3, realizable in the limit of high buffer strength and densely tethered films. Under these conditions, hybridization yields become insensitive to increases in analyte concentration even though many probes remain available to bind targets. These observations are attributed to the onset of packing constraints which, interestingly, become limiting significantly below maximum DNA coverages estimated from ideally efficient hexagonal packing. By delineating conditions under which specific hybridization behaviors are observed, the results advance fundamental knowledge in support of DNA microarray and biosensor applications.