We give a constructive proof of the finite version of Gowers’ FIN_k Theorem and analyze the corresponding upper bounds. The FIN_k Theorem is closely related to the oscillation stability of c_0. The stabilization of Lipschitz functions on arbitrary finite dimensional Banach spaces was proved well before by V. Milman. We compare the finite FIN_k Theorem with the Finite Stabilization Principle found by Milman in the case of spaces of the form ell_{infty}^n, ninN, and establish a much slower growing upper bound for the finite stabilization principle in this particular case.