  We consider what can be learnt about the processes of gas accretion and
depletion from the kinematic misalignment between the cold/warm gas and stars
in local early-type galaxies. Using simple analytic arguments and a toy model
of the processes involved, we show that the lack of objects with
counter-rotating gas reservoirs strongly constrains the relaxation, depletion
and accretion timescales of gas in early-type galaxies. Standard values of the
accretion rate, star formation efficiency and relaxation rate are not
simultaneously consistent with the observed distribution of kinematic
misalignments. To reproduce that distribution, both fast gas depletion ($t_{\rm
dep} <10^8$ yr; e.g. more efficient star formation) and fast gas destruction
(e.g. by active galactic nucleus feedback) can be invoked, but both also
require a high rate of gas-rich mergers ($>1$ Gyr$^{-1}$). Alternatively, the
relaxation of misaligned material could happen over very long timescales
($\simeq100$ dynamical times or $\approx1$-$5$ Gyr). We explore the various
physical processes that could lead to fast gas depletion and/or slow gas
relaxation, and discuss the prospects of using kinematic misalignments to probe
gas-rich accretion processes in the era of large integral-field spectroscopic
surveys.
