We present a comprehensive analysis of the technique of Longitudinal-Mode-Filling (LMF) to reduce Stimulated Brillouin Scattering (SBS) limitations in Ytterbium Doped Fibre Amplifiers (YDFA), for the generation of nanosecond, temporally shaped pulses. A basic Master-Oscillator-Power-Amplifier (MOPA) system, comprising an output YDFA with 10 µm-core active fibre, is experienced for benchmarking purposes. Input pulse-shaping is operated thanks to direct current modulation in highly multimode laser-diode seeds, either based on the use of Distributed Feed-Back (DFB) or of a Fibre Bragg Grating (FBG). These seeds enable wavelength control. We verify the effectiveness of the combination of LMF, with appropriate mode spacing, in combination with natural chirp effects from the seed to control the SBS threshold in a broad range of output energies, from a few to some tens of µJ. These variations are discussed versus all the parameters of the laser system. In accordance with the proposal of a couple of basic principles and with the addition of gain saturation effects along the active fibre, we develop a full-vectorial numerical model. Fine fits between experimental results and theoretical expectations are demonstrated. The only limitation of the technique arises from broadband beating noise, which is analysed thanks to a simplified, but fully representative description to discuss the signal-to-noise ratio of the amplified pulses. This provides efficient tools for application to the design of robust and cost-effective MOPAs, aiming to the generation of finely shaped and energetic nanosecond pulses without the need for any additional electro-optics.