  We extend the Bousfield-Kan spectral sequence for the computation of the
homotopy groups of the space of minimal A-infinity algebra structures on a
graded projective module. We use the new part to define obstructions to the
extension of truncated minimal A-infinity algebra structures. We also consider
the Bousfield-Kan spectral sequence for the moduli space of A-infinity
algebras. We compute up to the second page, terms and differentials, of these
spectral sequences in terms of Hochschild cohomology.
