  This paper compares three criteria for a spacetime to be free of position
drift: those by Hasse and Perlick (HP), Krasi\'nski and Bolejko (KB) and
Korzy\'nski and Kopi\'nski (KK). A spacetime having no position drift means
that every observer sees all light sources in unchanging directions. The
following is shown: (1) The HP criterion is a necessary condition for the KK
criterion to apply. (2) If the spacetime metric obeys the Einstein equations
with a perfect fluid source, then another necessary condition for the KK
criterion is the Weyl tensor being zero. (3) Result (2) points to the Stephani
metric, so it is shown that this metric obeys an equation which is still one
more necessary condition for the KK criterion. (4) The general Szekeres metrics
become drift-free by the KK criterion only in the Friedmann limit. (5) The HP
and KB criteria coincide, and the HP zero-drift condition imposes on the
Stephani metric the same restriction as found by Krasi\'nski and Bolejko (KB).
The relations between the three criteria are displayed and compared in a
diagram.
