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The pressing need for clinical diagnostics has required the development of novel nucleic acid-based detection technologies that are sensitive, fast, and inexpensive, and that can be deployed at point-of-care. Recently, the RNA-guided ribonuclease CRISPR-Cas13 has been successfully harnessed for such purposes. However, developing assays for detection of genetic variability, for example single-nucleotide polymorphisms, is still challenging and previously described design strategies are not always generalizable. Here, we expanded our characterization of LbuCas13a RNA-detection specificity by performing a combination of experimental RNA mismatch tolerance profiling, molecular dynamics simulations, protein, and crRNA engineering. We found certain positions in the crRNA-target-RNA duplex that are particularly sensitive to mismatches and establish the effect of RNA concentration in mismatch tolerance. Additionally, we determined that shortening the crRNA spacer or modifying the direct repeat of the crRNA leads to stricter specificities. Furthermore, we harnessed our understanding of LbuCas13a allosteric activation pathways through molecular dynamics and structure-guided engineering to develop novel Cas13a variants that display increased sensitivities to single-nucleotide mismatches. We deployed these Cas13a variants and crRNA design strategies to achieve superior discrimination of SARS-CoV-2 strains compared to wild-type LbuCas13a. Together, our work provides new design criteria and new Cas13a variants for easier-to-implement Cas13-based diagnostics.