In their 1987 paper Kraskiewicz and Pragacz defined certain modules, which we call KP modules, over the
upper triangular Lie algebra whose characters are Schubert polynomials. In a previous work the author showed that
the tensor product of Kraskiewicz-Pragacz modules always has KP filtration, i.e. a filtration whose each successive
quotients are isomorphic to KP modules. In this paper we explicitly construct such filtrations for certain special cases
of these tensor product modules, namely Sw Sd(Ki) and Sw Vd(Ki), corresponding to Pieri and dual Pieri rules for Schubert polynomials.