The multi-strange baryon yields in Pbbond" data-inlimg="/entities/sbnd" src="/sd/grey_pxl.gif" class="glyphImg imgLazyJSB">Pb collisions have been shown to exhibit an enhancement relative to pp reactions. In this work, Ξ and Ω production rates have been measured with the ALICE experiment as a function of transverse momentum, pT, in pbond" data-inlimg="/entities/sbnd" src="/sd/grey_pxl.gif" class="glyphImg imgLazyJSB">Pb collisions at a centre-of-mass energy of . The results cover the kinematic ranges 0.6 GeV/c<pT<7.2 GeV/c and 0.8 GeV/c<pT<5 GeV/c, for Ξ and Ω respectively, in the common rapidity interval 233cf0f6317de667943088c" title="Click to view the MathML source">−0.5<yCMS<0. Multi-strange baryons have been identified by reconstructing their weak decays into charged particles. The pT spectra are analysed as a function of event charged-particle multiplicity, which in pbond" data-inlimg="/entities/sbnd" src="/sd/grey_pxl.gif" class="glyphImg imgLazyJSB">Pb collisions ranges over one order of magnitude and lies between those observed in pp and Pbbond" data-inlimg="/entities/sbnd" src="/sd/grey_pxl.gif" class="glyphImg imgLazyJSB">Pb collisions. The measured pT distributions are compared to the expectations from a Blast-Wave model. The parameters which describe the production of lighter hadron species also describe the hyperon spectra in high multiplicity pbond" data-inlimg="/entities/sbnd" src="/sd/grey_pxl.gif" class="glyphImg imgLazyJSB">Pb collisions. The yield of hyperons relative to charged pions is studied and compared with results from pp and Pbbond" data-inlimg="/entities/sbnd" src="/sd/grey_pxl.gif" class="glyphImg imgLazyJSB">Pb collisions. A continuous increase in the yield ratios as a function of multiplicity is observed in pbond" data-inlimg="/entities/sbnd" src="/sd/grey_pxl.gif" class="glyphImg imgLazyJSB">Pb data, the values of which range from those measured in minimum bias pp to the ones in Pbbond" data-inlimg="/entities/sbnd" src="/sd/grey_pxl.gif" class="glyphImg imgLazyJSB">Pb collisions. A statistical model qualitatively describes this multiplicity dependence using a canonical suppression mechanism, in which the small volume causes a relative reduction of hadron production dependent on the strangeness content of the hyperon.