Let A be a commutative power-associative nilalgebra. In this paper we prove that when A (of characteristic ?2) is of dimension ? 8 and x? = 0 for all x ? A, then ((A²)²)² = 0. That is, A is solvable. We conclude that if A is of dimension ? 7 over a field of characteristic ?2, 3 and 5, then A is solvable.