An algebraic integer whose other conjugates over the field of the rationals Q are of modulus less than ε, where 0<ε ≦ 1, is called an ε-Pisot number. A Salem number is a real algebraic integer greater than 1 all of whose other conjugates over Q belong to the closed unit disc, with at least one of them of modulus 1. Let K be a number field generated over Q by a Salem number. We prove that there is a finite subset, say F_ε, of the integers of K such that each Salem number generating K over Q can be written as a sum of an element of F_ε and an ε-Pisot number. We also show some analytic properties of the set of ε-Pisot numbers.