  We examine the Kac-Schwarz problem of specification of point in Grassmannian
in the restricted case of gap-one first-order differential Kac-Schwarz
operators. While the pair of constraints satisfying $[{\cal K}_1,W] = 1$ always
leads to Kontsevich type models, in the case of $[{\cal K}_1,W] = W$ the
corresponding KP $\tau$-functions are represented as more sophisticated matrix
integrals.
