We propose and analyse numerically a novel dispersion-imbalanced non-linear optical loop mirror (NOLM) scheme allowing simultaneous compression and amplitude noise reduction of chirped ultrashort-pulsed signals. An all-fibre distributed Gires–Tournois etalon (DGTE) made of two uniform fibre Bragg gratings is inserted asymmetrically in the loop, and is used both to dispersion imbalance the NOLM and to compress the pulses. The results show that the output pulses are accompanied by side lobes, which originate from the no-uniformity of the DGTE dispersion spectrum. We analyse the formation of these side lobes and show that, in the case of highly chirped input pulses, side lobes are strongly reduced by the NOLM architecture. In this case, the device operates well even when the signal optical spectrum extends over an entire free spectral range of the DGTE. We believe that this work will be useful for the design of all-optical regeneration schemes for highly chirped data streams in optical transmission systems.