This paper shows that accurately optimised asymmetric three phase-shift (3PS)-distributed feedback (DFB) laser structures can strongly improve the stability of the single-longitudinal mode (SLM) operation, described by the mode selectivity and the flatness of the photon density profile, through an extended range of current injection, when compared to optimised symmetric 3PS-DFB structures reported elsewhere. This study reveals its importance in modern high bit-rate optical communication systems, by enhancing the possibility of attaining high performance DFB lasers, in easily fabricated structures. The procedure, based on matrix techniques, aims at the description of the optimal design of the laser structure and it is described step-by-step. Above-threshold calculations have been accomplished to evaluate the performance of the optimised asymmetric 3PS-DFB structure, namely: the mode selectivity ($G$), the flatness, the lasing wavelength, the optical power, and the side-mode suppression ratio (SMSR) evolutions with the current injection. For a current injection five times bigger than the threshold current, substantially improvements in $G$ (five times bigger) and in the SMSR (about 9 dB higher) are achieved when compared to similar, but symmetric, DFB structures.