Linked polyamides are a class of designed molecules that bind in the minor groove of double-stranded DNA in a partially sequence-specific manner but have limited sequence discriminatory abilities. This suggests a need for design alternatives to create molecules with enhanced sequence specificity. In this report we present formal proofs of the theoretical limits of the DNA sequence specificity of hypothetical sequence reading molecules as a function of their base recognition properties and sequence content and length of their target sequence. We prove that molecules containing nonspecific readers at critical positions within the molecule may have enhanced sequence specificity over molecules composed entirely of base specific reading elements. We also determine optimal patterns of base recognition for molecules in order to optimize their target sequence specificity. We also examine the effect of the length of a polyamide (i.e., the number of base pairs it binds) on its sequence discriminatory ability and determine necessary concentration dependent constraints on the binding free energies in order for longer polyamides to have greater sequence specificity than shorter ones. We show that unless the discriminatory ability of a ring for its preferred base is very strong, longer polyamides do not necessarily have greater sequence specificity over shorter ones when compared at the same molar concentration.