A detailed analytical investigation is made of the effect of nonlinear self-phase modulation in chirped-pulse-amplification-like schemes. It is demonstrated that self-phase modulation in the amplifier between the stretcher and the compressor breaks the dispersive sign symmetry of the configuration. This implies that, although self-phase modulation is usually considered a deleterious effect, different situations are possible, depending on the parameter regimes considered. In particular, the influence of self-phase modulation on the low-intensity wings of the compressed pulse may be more or less deleterious, depending on the dispersive sign combination of the stretcher and the compressor; in certain parameter regimes, it may in fact even enhance the pulse compression.