The invention relates to a package of performance additives for bitumen or bituminous compositions including an acidic adjuvant and a H2S scavenger chosen from organic or inorganic copper salts. The invention also relates to the use of said H2S scavenger in order to reduce the H2S emissions of bitumen or of a bituminous composition treated with the acidic adjuvant. The invention additionally relates to a process for the preparation of a bituminous composition. The preparation process according to the invention makes it possible to obtain bitumen/crosslinked polymer compositions having better mechanical and dynamic properties in comparison with the bitumen/crosslinked polymer compositions of the prior art, while substantially reducing the releases of hydrogen sulfide (H2S).