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The naive use of higher-order perturbation theory leads to the left-hand cut integrals in ππ dispersion relations [Phys. Lett. B 536 (2002) 59; B 549 (2002) 362; Nucl. Phys. A 695 (2001) 273] to be divergent. This problem is discussed and solved. We point out that the Adler zero condition imposes three constraints on the dispersion relations. The σ pole position is determined using the improved method, Mσ = 483± 13 Me V, Tσ = 705±50 Me V.The scattering length parameter is found to be in excellent agreement with the experimental result.