  In a domain $\Omega\subseteq \mathbb{R}^\mathbf{N}$ we consider compact,
Birman-Schwinger type, operators of the form
$\mathbf{T}_{P,\mathfrak{A}}=\mathfrak{A}^*P\mathfrak{A}$; here $P$ is a
singular Borel measure in $\Omega$ and $\mathfrak{A}$ is a noncritical order
$-l\ne -\mathbf{N}/2$ pseudodifferential operator. For a class of such
operators, we obtain estimates and a proper version of H.Weyl's asymptotic law
for eigenvalues, with order depending on dimensional characteristics of the
measure. A version of the CLR estimate for singular measures is proved. For
non-selfadjoint operators of the form $P_2 \mathfrak{A} P_1$ and
$\mathfrak{A}_2 P \mathfrak{A}_1$ with singular measures $P,P_1,P_2$ and
negative order pseudodifferential operators
$\mathfrak{A},\mathfrak{A}_1,\mathfrak{A}_2$ we obtain estimates for singular
numbers.
