We examine the use of high-throughput sequencing on binding sites recovered using a bacterial one-hybrid (B1H) system and find that improved models of transcription factor (TF) binding specificity can be obtained compared to standard methods of sequencing a small subset of the selected clones. We can obtain even more accurate binding models using a modified version of B1H selection method with constrained variation (CV-B1H). However, achieving these improved models using CV-B1H data required the development of a new method of analysis-GRaMS (Growth Rate Modeling of Specificity)-that estimates bacterial growth rates as a function of the quality of the recognition sequence. We benchmark these different methods of motif discovery using Zif268, a well-characterized C2H2 zinc-finger TF on both a 28bp randomized library for the standard B1H method and on 6bp randomized library for the CV-B1H method for which 45 different experimental conditions were tested: five time points and three different IPTG and 3-AT concentrations. We find that GRaMS analysis is robust to the different experimental parameters whereas other analysis methods give widely varying results depending on the conditions of the experiment. Finally, we demonstrate that the CV-B1H assay can be performed in liquid media, which produces recognition models that are similar in quality to sequences recovered from selection on solid media.