Absorbed hydrogen can dramatically increase hydrogenation activity of Pd nanoparticles and was predicted to do so also for Pt. This calls for investigations of the energetic stability of absorbed H in Pd and Pt using nanoparticle models as realistic as possible, i.e., (i) sufficiently large, (ii) supported, and (iii) precovered by hydrogen. Herein, hydrogen absorption is studied in MgO(100)-supported 1.6 nm large Pd and Pt nanoparticles with surfaces saturated by hydrogen. The effect of surface H on the stability of absorbed H is found to be significant and to exceed the effect of the support. H absorption is calculated to be endothermic in Pt, energy neutral in Pd(111) and bare Pd nanoparticles, and exothermic in H-covered Pd nanoparticles. Hence, we identify the abundance of surface H and the nanostructuring of Pd as prerequisites for facile absorption of hydrogen in Pd and for the concomitantly altered catalytic activity.