  For a nondegenerate quadratic form phi on a vector space V of dimension 2n +
1, let X_d be the variety of d-dimensional totally isotropic subspaces of V. We
give a sufficient condition for X_2 to be 2-incompressible, generalizing in a
natural way the known sufficient conditions for X_1 and X_n. Key ingredients in
the proof include the Chernousov-Merkurjev method of motivic decomposition as
well as Pragacz and Ratajski's characterization of the Chow ring of (X_2)_E,
where E is a field extension splitting phi.
