  We construct self-gravitating razor-thin disks of counterrotating dust around
Schwarzschild black holes (BHs) by applying the "displace, cut, and reflect"
method to known seed solutions representing multi-holes. All but one of the
sources of the seed solution generate the surrounding annular disk, whereas the
remaining BH is kept unaltered and lies at the disk center after the
transformation. The disks are infinite in extent, have annular character, and
are linearly stable up to the innermost stable circular orbit of the system.
Moreover, all energy conditions are satisfied along the disk and the spacetime
is asymptotically flat, having finite ADM mass. We also comment on charged
disks around extremal Reissner-Nordstr\"om BHs constructed from a
Majumdar-Papapetrou $N$-BH seed solution. These simple examples can be extended
to more general "BH + disk" solutions, obtained by the same method from seeds
of the type "BH + arbitrary axisymmetric source". A natural follow-up of this
work would be to construct disks around Reissner-Nordstr\"om BHs with arbitrary
charge-to-mass ratio and around Kerr BHs.
