  The spin-Peierls transition is modeled in the dimer phase of the spin-$1/2$
chain with exchanges $J_1$, $J_2 = \alpha J_1$ between first and second
neighbors. The degenerate ground state generates an energy cusp that
qualitatively changes the dimerization $\delta(T)$ compared to Peierls systems
with nondegenerate ground states. The parameters $J_1 = 160$ K, $\alpha = 0.35$
plus a lattice stiffness account for the magnetic susceptibility of CuGeO$_3$,
its specific heat anomaly, and the $T$ dependence of the lowest gap.
