  The ADR algebra $R_A$ of an Artin algebra $A$ is a right ultra strongly
quasihereditary algebra (RUSQ algebra). In this paper we study the
$\Delta$-filtrations of modules over RUSQ algebras and determine the projective
covers of a certain class of $R_A$-modules. As an application, we give a
counterexample to a claim by Auslander-Platzeck-Todorov, concerning projective
resolutions over the ADR algebra.
