The ability to generate RNA aptamers for synthetic biology using in vitro selection depends on the informational complexity (IC) needed to specify functional structures that bind target ligands with desired affinities in physiological concentrations of magnesium. We investigate how selection for high-affinity aptamers is constrained by chemical properties of the ligand and the need to bind in low magnesium. We select two sets of RNA aptamers that bind planar ligands with dissociation constants (Kds) ranging from 65 nM to 100 μM in physiological buffer conditions. Aptamers selected to bind the non-proteinogenic amino acid, p-amino phenylalanine (pAF), are larger and more informationally complex (i.e., rarer in a pool of random sequences) than aptamers selected to bind a larger fluorescent dye, tetramethylrhodamine (TMR). Interestingly, tighter binding aptamers show less dependence on magnesium than weaker-binding aptamers. Thus, selection for high-affinity binding may automatically lead to structures that are functional in physiological conditions (1–2.5 mM Mg2+). We hypothesize that selection for high-affinity binding in physiological conditions is primarily constrained by ligand characteristics such as molecular weight (MW) and the number of rotatable bonds. We suggest that it may be possible to estimate aptamer–ligand affinities and predict whether a particular aptamer-based design goal is achievable before performing the selection.