Self-collimated slow-sound propagation in a two-dimensional rectangular sonic crystal composed of elliptical scatterers in air is numerically demonstrated. The group velocity at the centre and the edges of the fourth acoustic band is reduced to 45 m s(-1) and 30 m s(-1), corresponding to 1/8 and 1/12 of the speed of sound in air, respectively. Elimination of omni-directional reflections encountered in linear waveguides and the reduction of group-velocity dispersion at the mid-band frequencies lead to preservation of pulse shape and amplitude upon traversal of the sonic crystal. Wave transmission is increased from approximately -20 to -2.5 dB, with almost an order of magnitude enhancement, via injector layers optimized through a pattern search algorithm. Self-collimating performance of the system is not degraded under oblique incidence, except for pulse broadening due to increased effective source width.