  In numerically constructing a spacetime that has an approximate timelike
Killing vector, it is useful to choose spacetime coordinates adapted to the
symmetry, so that the metric and matter variables vary only slowly with time in
these coordinates. In particular, this is a crucial issue in numerically
calculating a binary black hole inspiral. An approximate homothetic vector
plays a role in critical gravitational collapse. We summarize old and new
suggestions for finding such coordinates from a general point of view. We then
test some of these in various toy models with spherical symmetry, including
critical fluid collapse and critical scalar field collapse.
