  Hydrogen-rich Type II supernovae (SNe II) are the most frequently observed
class of core-collapse SNe (CCSNe). However, most studies that analyse large
samples of SNe II lack events with absolute peak magnitudes brighter than -18.5
mag at rest-frame optical wavelengths. Thanks to modern surveys, the detected
number of such luminous SNe II (LSNe II) is growing. There exist several
mechanisms that could produce luminous SNe II. The most popular propose either
the presence of a central engine (a magnetar gradually spinning down or a black
hole accreting fallback material) or the interaction of supernova ejecta with
circumstellar material (CSM) that turns kinetic energy into radiation energy.
In this work, we study the light curves and spectral series of a small sample
of six LSNe II that show peculiarities in their H$\alpha$ profile, to attempt
to understand the underlying powering mechanism. We favour an interaction
scenario with CSM that is not dense enough to be optically thick to electron
scattering on large scales -- thus, no narrow emission lines are observed. This
conclusion is based on the observed light curve (higher luminosity, fast
decline, blue colours) and spectral features (lack of persistent narrow lines,
broad H$\alpha$ emission, lack of H$\alpha$ absorption, weak or nonexistent
metal lines) together with comparison to other luminous events available in the
literature. We add to the growing evidence that transients powered by
ejecta-CSM interaction do not necessarily display persistent narrow emission
lines.
