  Harmonic coordinate conditions in stationary asymptotically flat spacetimes
with matter sources have more than one solution. The solutions depend on the
degree of smoothness of the metric and its first derivatives, which we wish to
impose across the material boundary, and on the conditions at infinity and at a
suitable point inside the matter. This is illustrated in detail by simple fully
solvable examples of static spherically symmetric spacetimes in global harmonic
coordinates. Examples of stationary electrovacuum spacetimes described simply
in harmonic coordinates are also given. They can represent the exterior fields
of material discs.
  The use of an appropriate background metric considerably simplifies the
calculations.
