The use of a composition including a transition metal salt and at least one water-soluble aldehyde or water-soluble aldehyde precursor scavenges H2S that is present in aqueous fluids (e.g. produced water liquid streams), natural gas and in oil and mixtures thereof (e.g. mixed production streams that contain all three phases) better than either component when used alone. The resulting scavenger combination significantly increases the reaction rate and the overall scavenging efficiency, i.e. capacity over the case where each component is used alone, in the same total amount. Non-limiting examples of the metal salt include zinc or iron carboxylates, and a non-limiting example of a water-soluble aldehyde or water-soluble aldehyde precursor is ethylene glycol hemiformal.