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We formulate an alternative form of threshold harvesting and investigate its properties within the framework of a predator–prey model. Our formulation accounts for economic constraints and is defined as a continuous harvesting function of the predator species. Theoretical and numerical analysis indicate that our formulation, which we call continuous threshold policy (CTP), can help improve undesirable behavior of the predator–prey ecosystem. Our study includes uniform boundedness of solutions, stability of equilibria and periodic orbits, bifurcations, and heteroclinic orbits.