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We present optical and near-IR data of three Type II supernovae (SNe II), SN2008bm, SN 2009aj, and SN 2009au. These SNe display the following commoncharacteristics: signs of early interaction of the ejecta with circumstellarmaterial (CSM), blue $B\!-\!V$ colours, weakness of metal lines, low expansionvelocities, and $V$-band absolute magnitudes 2-3 mag brighter than thoseexpected for normal SNe II based on their expansion velocities. Two more SNereported in the literature (SN 1983K and LSQ13fn) share properties similar toour sample. Analysing this set of five SNe II, which are luminous for their lowexpansion velocities (LLEV), we find that their properties can be reproducedassuming ejecta-CSM interaction that lasts between 4-11 weeks post explosion.The contribution of this interaction to the radiation field seems to be thedominant component determining the observed weakness of metal lines in thespectra rather than the progenitor metallicity. Based on hydrodynamicsimulations, we find that the interaction of the ejecta with a CSM of ~3.6M$_\odot$ can reproduce the light curves and expansion velocities of SN 2009aj.Using data collected by the Chilean Automatic Supernova Search, we estimate anupper limit for the LLEV SNe II fraction to be 2-4 per cent of all normal SNeII. With the current data-set, it is not clear whether the LLEV events are aseparated class of SNe II with a different progenitor system, or whether theyare the extreme of a continuum mediated by CSM interaction with the rest of thenormal SN II population.

Luminous Type II supernovae for their low expansion velocities