A common approach to theory testing in experimental psychology relies on null hypothesis significance testing via (generalized) linear regression models. We showcase order-constrained methods as an alternative route to behavioral decision analytics. Order-constrained inference can improve the precision and nuance of theory testing. For example, the method can be leveraged to quantify the evidence in support of, or against, a given hypothesis. It also offers advanced model selection tools for quantitative competition among multiple theories. To illustrate our case for order-constrained methods, we re-analyze data from a pre-registered experiment on incentives, cognitive reflection, and dishonest behavior. Using this example, we advocate for order-constrained inference as a tool for researchers to better tailor their analytical procedure to the theory under investigation. This allows them to eschew arbitrary auxiliary assumptions on the theoretical level whose only purpose is to legitimize the statistical model underlying conventional analyses. We further highlight the advantages of Bayesian order-constrained inference and show how, in an experimental setting, it can deliver more convincing and more nuanced evidence than frequentist null hypothesis significance testing. This also opens new avenues of research for supplementing and expanding experimental designs in psychological research.