A capture mass for heavy metals, in particular mercury, contained in a gaseous or liquid feed, said mass comprising: copper which is present at least in part in the sulphide form, CuxSy, a porous support based on alumina; characterized in that said porous support has a total pore volume (TPV) in the range 0.8 to 1.5 cm3/g, a mesopore volume (V6 nm-100 nm) in the range 0.5 to 1.3 cm3/g, and a macropore volume (V100 nm) in the range 0.33 to 0.45 cm3/g, it being understood that the ratio between the mesopore volume and the macropore volume (V6 nm-100 nm/V100 nm) is in the range 1 to 5.