  The diversity of Type II supernovae (SNe II) is thought to be driven mainly
by differences in their progenitor's hydrogen-rich (H-rich) envelope mass, with
SNe IIP having long plateaus ($\sim100$ days) and the most massive H-rich
envelopes. However, it is an ongoing mystery why SNe II with short plateaus
(tens of days) are rarely seen. Here, we present optical/near-infrared
photometric and spectroscopic observations of luminous Type II short-plateau
SNe 2006Y, 2006ai, and 2016egz. Their plateaus of about $50$-$70$ days and
luminous optical peaks ($\lesssim-18.4$ mag) indicate significant pre-explosion
mass loss resulting in partially stripped H-rich envelopes and early
circumstellar material (CSM) interaction. We compute a large grid of
MESA+STELLA single-star progenitor and light-curve models with various
progenitor zero-age main-sequence (ZAMS) masses, mass-loss efficiencies,
explosion energies, $^{56}$Ni masses, and CSM densities. Our model grid shows a
continuous population of SNe IIP-IIL-IIb-like light-curve morphology in
descending order of H-rich envelope mass. With large $^{56}$Ni masses
($\gtrsim0.05\,M_\odot$), short-plateau SNe II lie in a confined parameter
space as a transitional class between SNe IIL and IIb. For SNe 2006Y, 2006ai,
and 2016egz, our findings suggest high-mass red supergiant (RSG) progenitors
($M_{\rm ZAMS} \simeq 18$-$22\,M_{\odot}$) with small H-rich envelope masses
($M_{\rm H_{\rm env}} \simeq 1.7\,M_{\odot}$) that have experienced enhanced
mass loss ($\dot{M} \simeq 10^{-2}\,M_{\odot}\,{\rm yr}^{-1}$) for the last few
decades before the explosion. If high-mass RSGs result in rare short-plateau
SNe II, then these events might ease some of the apparent underrepresentation
of higher-luminosity RSGs in observed SN II progenitor samples.
