  We affirmatively settle the question on existence of a real-valued spectral
shift function for a pair of self-adjoint operators $H$ and $V$ such that $V$
is bounded and $V(H-iI)^{-1}$ belongs to a Schatten-von Neumann ideal $\S^n$ of
compact operators in a separable Hilbert space. We also show that the function
satisfies the same trace formula as in the known case of $V\in\S^n$ and that it
is unique up to a polynomial summand of order $n-1$. Our results significantly
advance earlier partial results where counterparts of the spectral shift
function for noncompact perturbations lacked real-valuedness and aforementioned
uniqueness as well as appeared in more complicated trace formulas for much more
restrictive sets of functions.
