A novel way to design tapered nonlinear refractive indices capable to compensate the deterioration of second order bright spatial solitons in a medium with two-photon absorption (TPA), is presented in detail. At first it is shown the effect of TPA over such solitons and then, using a step-by-step adaptive algorithm, we computed the corresponding nonlinear refractive index variation able to keep the beam's shape and its confinement. This process has proved to be effective and the adaptive algorithm proposed here could certainly be useful for other applications in photonics.