The possibilities and limitations of linear compression of positively chirped pulses in the negative-dispersion region of a step-index large mode-area single-mode optical fibre are investigated for the first time. Analytical formulae for critical values of radiation power are found, below which pedestal-free pulse compression is possible down to the Fourier limit. It is demonstrated that at radiation powers exceeding these critical values, there exists an optimal compressing fibre length, over which laser pulses reach the minimum of the time-bandwidth product, and beyond which irreversible pulse deformation occurs. The modelling results agree well with the experimental data.