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Critical stability constraints are a small set of conditions that are enough to maintain the stability of a system when some parameters are perturbed from a nominal stable setting. The paper uses a recently introduced efficient integer-preserving (IP) form of the Bistritz test to derive critical constraints for stability of discrete-time linear systems. The new procedure produces polynomial (rather than rational) constraints of particularly low degree whose variates are the free parameters (or the literal coefficients) of the system's characteristic polynomial. Comparison with the modified Jury test, also an efficient IP stability test, shows that the constraints are obtained with less computation and, more contributing to simplicity, the constraints appear as polynomials with degrees lower by a factor of two.