  Context: Maser emission from the H2O molecule probes the warm, inner
circumstellar envelopes of oxygen-rich red giant and supergiant stars.
Multi-maser transition studies can be used to put constraints on the density
and temperature of the emission regions.
  Aims: A number of known H2O maser lines were observed toward the long period
variables R Leo and W Hya and the red supergiant VY CMa. A search for a new,
not yet detected line near 475 GHz was conducted toward these stars.
  Methods: The Atacama Pathfinder Experiment telescope was used for a
multi-transition observational study of submillimeter H2O lines.
  Results: The 5_33-4_40 transition near 475 GHz was clearly detected toward VY
CMa and W Hya. Many other H2O lines were detected toward all three target
stars. Relative line intensity ratios and velocity widths were found to vary
significantly from star to star.
  Conclusions: Maser action is observed in all but one line for which it was
theoretically predicted. In contrast, one of the strongest maser lines, in R
Leo by far the strongest, the 437 GHz 7_53-6_60 transition, is not predicted to
be inverted. Some other qualitative predictions of the model calculations are
at variance with our observations. Plausible reasons for this are discussed.
Based on our findings for W Hya and VY CMa, we find evidence that the H2O
masers in the AGB star W Hya arise from the regular circumstellar outflow,
while shock excitation in a high velocity flow seems to be required to excite
masers far from the red supergiant VY CMa.
