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Near-threshold bound states are often characterized by a small set of low-energy parameters, yet multiple microscopic pictures can reproduce them. This talk uses a solvable finite-range scattering model to show how these parameters can be extracted and then reproduced within an effective field theory that includes an explicit auxiliary field. The comparison yields a transparent connection between model parameters and the effective-range expansion, and it helps identify which EFT terms are essential for a realistic description in the case of the deuteron. The final part of the talk outlines how the same strategy can be applied to exotic hadronic bound states close to threshold, focusing on X(3872) in a molecular interpretation