We prove that the present experimental constraints are already enough to rule out the possibility of the ~125 GeV Higgs found at LHC being the second lightest Higgs in a general MSSM context, even with explicit CP violation in the Higgs potential. Contrary to previous studies, we are able to eliminate this possibility analytically, using simple expressions for a relatively small number of observables. We show that the present LHC constraints on the diphoton signal strength, tau-tau production through Higgs and BR(B -> X_s gamma) are enough to preclude the possibility of H_2 being the observed Higgs with m_H~125 GeV within an MSSM context, without leaving room for finely tuned cancellations. As a by-product, we also comment on the difficulties of an MSSM interpretation of the excess in the gamma-gamma production cross section recently found at CMS that could correspond to a second Higgs resonance at m_H~136 GeV.