  We give a full metric describing the gravitational field of a static and
axisymmetric thin disk without radial pressure encircling a Schwarzschild black
hole. The disk density profiles are astrophysically realistic, stretching from
the horizon to radial infinity, yet falling off quickly at both these
locations. The metric functions are expressed as finite series of Legendre
polynomials. Main advantages of the solution are that (i) the disks have no
edges, so their fields are everywhere regular (outside the horizon), and that
(ii) all non-trivial metric functions are provided analytically and in closed
forms. We examine and illustrate basic properties of the black-hole -- disk
space-times.
