Single molecule localization based super-resolution (SM-SR) imaging techniques require robust identification and accurate localization of single molecules to yield reliable emitter position estimates for further quantitative analysis. One of the key steps of SM-SR analysis is to clearly identify isolated, single emitters such that obtained localizations relate to actual single molecule locations, and are not influenced by signal from nearby or overlapping fluorophores. We refer to the process of identifying and discarding sub-regions that contain overlapping fluorophores as the rejection algorithm.We show that even at an optimal active emitter density, more than 50% of the emitters cannot be isolated such to give an unbiased estimate of position. Furthermore, it is possible that even for the case of isolated single emitters, the fitting routine may not converge and thus provides incorrect localizations. A robust, statistically rigorous rejection algorithm that compares the fitted model to the data is necessary to avoid incorrect or biased localizations and is essential for the success of quantitative analysis.Here, we show that the Log-likelihood Ratio (LLR) is a preferred metric for rejection algorithms and that p-values can be calculated and used for statistical significance tests when the distribution of the LLR under low signal conditions is correctly modeled. We compare the LLR with other commonly used rejection algorithms such as the elliptical or sum of squared error tests. As a demonstration, we show the improved resolution in reconstructed super-resolution images when using the LLR rejection algorithm as compared with those generated using other rejection algorithms.