  The $m \alpha^6$ correction to energy is expressed in terms of an effective
Hamiltonian $H^{(6)}$ for an arbitrary state of helium. Numerical calculations
are performed for $n=2$ levels, and the previous result for the $2^3P$ centroid
is corrected. While the resulting theoretical predictions for the ionization
energy are in moderate agreement with experimental values for $2^3S_1$, $2^3P$,
and $2^1S_0$ states, they are in significant disagreement for the singlet state
$2^1P_1$.
