In this article, three new inter-symbol interference (ISI)-free pulses with enhanced performance compared to the state-of-the-art are proposed and studied in terms of frequency and time domain characteristics. They are based on inverse hyperbolic functions and on the concept of inner and outer functions, which was first introduced by the authors. New pulses are two-parametric, i.e., their design depends only on the roll-off factor and the timing jitter parameter, and they outperform most of the well-known pulses reported in the literature, since they present lower error probability, smaller maximum distortion and wider eye-diagram.