The situation of a liquid jet issuing into a quiescent medium of different density and viscosity is one that occurs in several natural systems (estuaries, undersea vents) and engineering systems (chemical processing, plasma torches). Low-density jets have been well studied in the literature, and the onset of self-sustained oscillations ('global modes') have been strongly correlated with the presence of absolutely unstable profiles of velocity and density in the near-field of the jet. The case of viscosity variation has received less attention. Work in our lab focuses on performing linear stability calculations that predict the absolute instability in a jet as a function of jet velocity profile and viscosity ratio. Simultaneously, experiments track the onset of global modes as a function of Reynolds number and viscosity ratio. Low-viscosity jets appear to breakdown through the appearance of a helical mode that has not been reported for constant property jets.