Nucleic acid-based aptamers possess many useful features that make them a promising alternative to antibodies and other affinity reagents, including well-established chemical synthesis, reversible folding, thermal stability and low cost. However, the selection process typically used to generate aptamers (SELEX) often requires significant resources and can fail to yield aptamers with sufficient affinity and specificity. A number of seminal theoretical models and numerical simulations have been reported in the literature offering insights into experimental factors that govern the effectiveness of the selection process. Though useful, these previous models have not considered the full spectrum of experimental factors or the potential impact of tuning these parameters at each round over the course of a multi-round selection process. We have developed an improved mathematical model to address this important question, and report that both target concentration and the degree of non-specific background binding are critical determinants of SELEX efficiency. Although smaller target concentrations should theoretically offer superior selection outcome, we show that the level of background binding dramatically affect the target concentration that will yield maximum enrichment at each round of selection. Thus, our model enables experimentalists to determine appropriate target concentrations as a means for protocol optimization. Finally, we perform a comparative analysis of two different selection methods over multiple rounds of selection, and show that methods with inherently lower background binding offer dramatic advantages in selection efficiency.