We present a new HI modelling tool called textsc{Galactus}. The program has been designed to perform automated fits of disc-galaxy models to observations. It includes a treatment for the self-absorption of the gas. The software has been released into the public domain. We describe the design philosophy and inner workings of the program. After this, we model the face-on galaxy NGC2403, using both self-absorption and optically thin models, showing that self-absorption occurs even in face-on galaxies. It is shown that the maximum surface brightness plateaus seen in Paper I of this series are indeed signs of self-absorption. The apparent HI mass of an edge-on galaxy can be drastically lower compared to that same galaxy seen face-on. The Tully-Fisher relation is found to be relatively free from self-absorption issues.
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