  We construct some spectral sequences as tools for computing commutative
cohomology of commutative Lie algebras in characteristic 2. In a first part, we
focus on a Hochschild-Serre-type spectral sequence, while in a second part we
obtain comparison spectral sequences which mediate between
Chevalley-Eilenberg-, commutative-and Leibniz cohomology. These methods are
illustrated by a few computations.
