K-orbits on G/B and Schubert constants for pairs of signed shuffles in types C and D

We give positive descriptions for certain Schubert structure constants for the full flag variety in Lie types C and D. This is accomplished by first observing that a number of the K=GL(n,C)-orbit closures on these flag varieties coincide with Richardson varieties, and then applying a theorem of M. Brion on the decomposition of such an orbit closure in the Schubert basis in terms of paths in the weak order graph.