It is well known that Kazhdan-Lusztig polynomials measure singularities of Schubert varieties. More precisely, coefficients of these polynomials count dimensions of local intersection cohomology groups of the varieties. A fundamental property of these dimensions is that they increase (weakly) as one moves down a fixed Schubert variety. Recently Wyser and Yong have asked whether the corresponding property holds of K-orbit closures in flag varieties. I will give an affirmative answer in certain cases.)