  We investigate the padded version of reduction, an extension of multifraction
reduction as defined in arXiv:1606.08991, and connect it both with ordinary
reduction and with the so-called Property $\mathrm{H}$. As an application, we
show that all Artin-Tits groups of sufficiently large type satisfy some
weakening Conjecture $\mathrm{A^{padded}}$ of Conjecture $\mathrm{A}$, thus
showing that the reduction approach is relevant for these groups.
