  The empirical upper luminosity boundary $L_{\rm max}$ of cool supergiants,
often referred to as the Humphreys-Davidson limit, is thought to encode
information on the general mass-loss behaviour of massive stars. Further, it
delineates the boundary at which single stars will end their lives stripped of
their hydrogen-rich envelope, which in turn is a key factor in the relative
rates of Type-II to Type-Ibc supernovae from single star channels. In this
paper we have revisited the issue of $L_{\rm max}$ by studying the luminosity
distributions of cool supergiants (SGs) in the Large and Small Magellanic
Clouds (LMC/SMC). We assemble samples of cool SGs in each galaxy which are
highly-complete above $\log L/L_{\odot}$=5.0, and determine their spectral
energy distributions from the optical to the mid-infrared using modern
multi-wavelength survey data. We show that in both cases $L_{\rm max}$ appears
to be lower than previously quoted, and is in the region of $\log
L/L_{\odot}$=5.5. There is no evidence for $L_{\rm max}$ being higher in the
SMC than in the LMC, as would be expected if metallicity-dependent winds were
the dominant factor in the stripping of stellar envelopes. We also show that
$L_{\rm max}$ aligns with the lowest luminosity of single nitrogen-rich
Wolf-Rayet stars, indicating of a change in evolutionary sequence for stars
above a critical mass. From population synthesis analysis we show that the
Geneva evolutionary models greatly over-predict the numbers of cool SGs in the
SMC. We also argue that the trend of earlier average spectral types of cool SGs
in lower metallicity environments represents a genuine shift to hotter
temperatures. Finally, we use our new bolometric luminosity measurements to
provide updated bolometric corrections for cool supergiants.
