The DNA-binding interfaces of the androgen (AR) and glucocorticoid (GR) receptors are virtually identical, yet these transcription factors share only about a third of their genomic binding sites and regulate similarly distinct sets of target genes. To address this paradox, we determined the intrinsic specificities of the AR and GR DNA-binding domains using a refined version of SELEX-seq. We developed an algorithm, SelexGLM, that quantifies binding specificity over a large (31-bp) binding site by iteratively fitting a feature-based generalized linear model to SELEX probe counts. This analysis revealed that the DNA-binding preferences of AR and GR homodimers differ significantly, both within and outside the 15-bp core binding site. The relative preference between the two factors can be tuned over a wide range by changing the DNA sequence, with AR more sensitive to sequence changes than GR. The specificity of AR extends to the regions flanking the core 15-bp site, where isothermal calorimetry measurements reveal that affinity is augmented by enthalpy-driven readout of poly(A) sequences associated with narrowed minor groove width. We conclude that the increased specificity of AR is correlated with more enthalpy-driven binding than GR. The binding models help explain differences in AR and GR genomic binding and provide a biophysical rationale for how promiscuous binding by GR allows functional substitution for AR in some castration-resistant prostate cancers.