We show that the mass-segregation solution for the steady state distribution of stars around a massive black hole (MBH) has two branches: the well-known weak segregation solution \citepbah+77, and a strong segregation solution, which is analyzed here for the first time. The nature of the solution depends on the heavy-to-light stellar mass ratio M_H/M_L and on the unbound population number ratio N_H/N_L, through the relaxational coupling parameter DELTA = 4N_HM_H2<=ft/<=ft[N_LM_L2(3 + M_H/M_L)\right]\ri ght.. When the heavy stars are relatively common ( DELTA \gg 1), they scatter frequently on each other. This efficient self-coupling leads to weak mass segregation, where the stars form n \propto r- alpha _M mass-dependent cusps near the MBH, with indices alpha _H = 7/4 for the heavy stars and 3/2 < alpha _L < 7/4 for the light stars (i.e. \max( alpha _H - alpha _L) 1/4). However, when the heavy stars are relatively rare ( DELTA \ll 1), they scatter mostly on light stars, sink to the center by dynamical friction and settle into a much steeper cusp with 2 <=sssim alpha _H <=sssim 11/4, while the light stars form a 3/2 < alpha _L < 7/4 cusp, resulting in strong segregation (i.e. \max( alpha _H - alpha _L) 1). We show that the present-day mass function of evolved stellar populations with a universal initial mass function (coeval or continuously star forming) separate into two distinct mass scales, 1 \Mo of main sequence and compact dwarfs, and 10 \Mo of stellar black holes (SBHs), and have DELTA < 0.1. We conclude that it is likely that many relaxed galactic nuclei are strongly segregated. We review indications of strong segregation in observations of the Galactic Center and in results of numeric simulations, and briefly list possible implications of a very high central concentration of SBHs around a MBH.