  I study the behaviour of the maximum rms fractional amplitude, $r_{\rm max}$
and the maximum coherence, $Q_{\rm max}$, of the kilohertz quasi-periodic
oscillations (kHz QPOs) in a dozen low-mass X-ray binaries. I find that: (i)
The maximum rms amplitudes of the lower and the upper kHz QPO, $r^{\ell}_{\rm
max}$ and $r^{\rm u}_{\rm max}$, respectively, decrease more or less
exponentially with increasing luminosity of the source; (ii) the maximum
coherence of the lower kHz QPO, $Q^{\ell}_{\rm max}$, first increases and then
decreases exponentially with luminosity, at a faster rate than both
$r^{\ell}_{\rm max}$ and $r^{\rm u}_{\rm max}$; (iii) the maximum coherence of
the upper kHz QPO, $Q^{\rm u}_{\rm max}$, is more or less independent of
luminosity; and (iv) $r_{\rm max}$ and $Q_{\rm max}$ show the opposite
behaviour with hardness of the source, consistent with the fact that there is a
general anticorrelation between luminosity and spectral hardness in these
sources. Both $r_{\rm max}$ and $Q_{\rm max}$ in the sample of sources, and the
rms amplitude and coherence of the kHz QPOs in individual sources show a
similar behaviour with hardness. This similarity argues against the
interpretation that the drop of coherence and rms amplitude of the lower kHz
QPO at high QPO frequencies in individual sources is a signature of the
innermost stable circular orbit around a neutron star. I discuss possible
interpretations of these results in terms of the modulation mechanisms that may
be responsible for the observed variability.
