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Cu/W composites are widely used in various industrial fields as they show thermomechanical properties suitable for a wide range of applications. Additionally, in semiconductor products, WTi in contact with Cu acts as a barrier material between Cu and Si/SiO2. Therefore, the bonding behavior of both Cu/W and Cu/WTi is of great economical interest, also with respect to the effects that impurities could have on the behaviour of the Cu/W(Ti) interface. The segregation behavior of relevant impurities has not been studied in detail before. In this work, we create atomistic models of the Cu/W and Cu/WTi interfaces, compare their energetics to previously known interfaces and study the effect of segregation on the interface cohesion. We find that all investigated segregants, i.e. Ti, Cl, S, Al, H, O, and vacancies weaken the cohesion of the interface.