Results of super-exponential pulse propagation in dispersion dominant regime of single mode fiber are presented, both for initially un-chirped and chirped cases. Split-step Fourier model for nonlinear Schrödinger equation was used for this purpose. Results clearly show that an initially un-chirped pulse first goes on compression and then broadens at higher rate if the steepness parameter goes on increasing. Results also show that for a fixed value of the steepness parameter, however larger than unity, the narrowing of the pulse experiences only for zero or negative values of initial chirp. These investigations provide a deeper insight for the fiber response to such type of optical pulses.