  Wisdom has recently unveiled a new relativistic effect, called ``spacetime
swimming'', where quasi-rigid free bodies in curved spacetimes can "speed up",
"slow down" or "deviate" their falls by performing "local" cyclic shape
deformations. We show here that for fast enough cycles this effect dominates
over a non-relativistic related one, named here ``space swinging'', where the
fall is altered through "nonlocal" cyclic deformations in Newtonian
gravitational fields. We expect, therefore, to clarify the distinction between
both effects leaving no room to controversy. Moreover, the leading contribution
to the swimming effect predicted by Wisdom is enriched with a higher order term
and the whole result is generalized to be applicable in cases where the tripod
is in large red-shift regions.
