We study analytically pulse distortion in linear slow light systems, and provide some useful limits on these devices. Additionally, we also show that the contributions of phase and amplitude broadening can be de-coupled and quantified. It is observed that phase broadening is generally smaller than amplitude broadening in conventional slow light media (lorentzian gain profile) except for very large fractional delays, where it becomes larger. Upon these expressions, we may envisage new strategies to minimize the distortion in the delaying of pulses, depending on the specific application and the required fractional delay. To overcome the residual distortion, we show that nonlinear systems can lead to a resharpening of the pulses and a re-generation of the filtered frequencies.