Decoders for brain-computer interfaces (BCIs) assume constraints on neural activity, chosen to reflect scientific beliefs while yielding tractable computations. We document how low tangling – a typical property of motor-cortex neural trajectories – yields unusual neural geometries. We designed a decoder, MINT, to embrace appropriate statistical constraints for these geometries. MINT takes a trajectory-centric approach: a library of neural trajectories (rather than a set of neural dimensions) provides a scaffold approximating the neural manifold. Each neural trajectory has a corresponding behavioral trajectory, allowing straightforward but highly nonlinear decoding. MINT outperformed other interpretable methods, and outperformed expressive machine learning methods in 37 of 42 comparisons. Yet unlike such methods MINT's constraints are known, not the implicit result of optimizing decoder output. MINT performed well across tasks, suggesting its assumptions are generally well-matched to the statistics of neural data. Despite embracing highly nonlinear relationships between behavior and potentially complex neural trajectories, MINT's computations are simple, scalable, and provide interpretable quantities such as data likelihoods. MINT's performance and simplicity suggest it may be an excellent candidate for clinical BCI applications.