We address the computation of Γ_Z and of the intriguing quantity R_b in the MSSM including full treatment of the Higgs sector. For a pseudoscalar Higgs mass m_A^0>70 GeV and CDF limits on m_t, the bounds on R_b at 1σ level leave no room to the MSSM to solve the 'R_b crisis' for any combination of the parameters, not even admitting the possibility of a light chargino and a light stop of O(50) GeV; however, for m_t not restricted by CDF, a 'tangential' solution exists in the window 2m_t/m_b. Our

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... eneral conclusion is that, if there is a 'R_b crisis' at all, its solution within the MSSM has to do more with the peculiar structure of the SUSY Higgs sector rather than with the spectrum of genuine supersymmetric particles. In view of the range predicted for m_A^0, LEP 200 should be able to definitely settle down this question.