The use of Ta/TaN barrier bilayer systems in electronic applications has been ubiquitous over the last decade. Alternative materials such as Co-W or Ru-W alloys have gathered interest as possible replacements due to their conjugation of favourable electrical properties and barrier layer efficiency at reduced thicknesses while enabling seedless Cu electroplating. The microstructure, morphology, and electrical properties of Cu films directly electrodeposited onto Co-W or Ru-W are important to assess, concomitant with their ability to withstand the electroplating baths/conditions. This work investigates the effects of the current application method and pH value of the electroplating solution on the electrocrystallisation behaviour of Cu deposited onto a Co-W barrier layer. The film structure, morphology, and chemical composition were studied by X-ray diffraction, scanning electron microscopy and atomic force microscopy, as well as photoelectron spectroscopy. The results show that the electrolyte solution at pH 1.8 is incapable of creating a compact Cu film over the Co-W layer in either pulsed or direct-current modes. At higher pH, a continuous film is formed. A mechanism is proposed for the nucleation and growth of Cu on Co-W, where a balance between Cu nucleation, growth, and preferential Co dissolution dictates the substrate area coverage and compactness of the electrodeposited films.