The attainable performance of inkjet printheads is severely limited by residual vibrations and cross-talk. Both effects are inseparably linked with the actuation of an ink channel. Residual vibrations occur each time a droplet has been jetted and, while actuating a channel, fluid-mechanics in neighboring channels are excited also. These phenomena affect the performance negatively, e.g. in terms of drop-consistency and achievable jetting frequencies. Previous work has shown that Iterative Learning Control (ILC) can be applied to design input wave forms (pulses) that leave the droplet formation undisturbed while minimizing these operational issues. However, the resulting pulses are usually too complex to be implemented on the Application Specific Integrated Circuit (ASIC) of a printhead. In this paper, the ILC control framework is adjusted with a modified algorithm that allows for the design of pulses with predefined complexity. It is demonstrated that this modified ILC using only piece-wise affine command signals operates without a severe loss of performance compared to unconstrained ILC. This paper shows the modeling required for ILC, the design of the controller, and the accompanying experimental results that show the minimization of residual vibrations as well as cross-talk.