The competition between nonmagnetic spin-Peierls (SP) and magnetic Néel ground states has been investigated in CuGeO3 doped with Zn, Ni, Mn, and Si. The analysis of specific heat, Cp, data in CuGeO3, measured as a function of magnetic field, supports a SP transition at TSP=14K. The replacement of Cu2+ by Zn2+, Ni2+, or Mn2+ reduces TSP and stabilizes a Néel state, not a spin-glass phase as previously suggested. No significant difference in Cp was observed for Zn- and Ni-doped samples. We suggest that the Néel state depends on |S-S|, where S is the spin of the dopant and S=12. © 1995 The American Physical Society.