We investigate the effects of viscoelasticity on drop generation in inkjet printing. In drop-on-demand printing, individual ink 'drops' are ejected from a nozzle by imposed pressure pulses. Upon exiting the nozzle, the shape of each 'drop' is that of a nearly spherical bead with a long thin trailing ligament. This ligament subsequently breaks up under the Rayleigh instability, typically into several small droplets (known as satellite drops). These satellite drops can create unwanted splash on the target substrate and a reduction in printing quality. Satellite drops can potentially be eliminated by adding polymer to the ink; elastic stresses can act to contract the trailing ligament into the main drop before capillary breakup occurs. However, elasticity can also reduce the drop velocity and can delay or even prevent the break-off of the drop from the ink reservoir within the nozzle. To achieve optimal drop shape and speed, non-Newtonian parameters such as the polymer concentration and molecular weight must be chosen correctly. We explore this parameter space via numerical simulations, using the Lagrangian-Eulerian finite-element method of Harlen et al. (J Non-Newtonian Fluid Mech 60:81-104, 1995). Results are compared with experimental observations taken from real printheads.