We investigate the influence of fluid properties on jet breakup in the context of drop-on-demand inkjet printing. In drop-ondemand printing, each drop remains connected to the printhead by a ligament which thins while the drop is in flight. Upon pinchoff the severed ligament may recoil into the leading drop, or (more commonly for high-speed printing) the ligament may fragment into ‘satellite drops’ which reduce printing resolution. A key goal of inkjet research is to prevent or impede the creation of satellite drops without compromizing on printing speed. Viscoelastic and shear-thinning fluids may, in rather different ways, exhibit enhanced resistance to fragmentation in jetting flows compared to Newtonian fluids of similar viscosity. In this work we seek to explore and exploit this behaviour with the overall aim of increasing the proportion of ejected ink contained within the main drop when printing at a prescribed drop velocity. Using Lagrangian finite-element simulations under realistic industrial inkjet conditions, we consider a non-Newtonian fluid model which incorporates both viscoelastic and thixotropic effects simultaneously. We discuss how appropriate values of the rheological parameters may be chosen so as to optimize the fluid's transient viscosity at different key stages of a drop-on-demand flow cycle, and how our results may be beneficial to industrial and commercial applications of inkjet technology.