  In this paper we study the Lindley-type equation $W=\max\{0, B - A - W\}$.
Its main characteristic is that it is a non-increasing monotone function in its
main argument $W$. Our main goal is to derive a closed-form expression of the
steady-state distribution of $W$. In general this is not possible, so we shall
state a sufficient condition that allows us to do so. We also examine stability
issues, derive the tail behaviour of $W$, and briefly discuss how one can
iteratively solve this equation by using a contraction mapping.
