The CVD process for the spinning of carbon nanotube (CNT) fibres combines the nucleation, growth and aggregation of CNTs in the form of an aerogel with fibre spinning into a single process step. The optimisation of the process requires agility in multi-dimensional parameter space, so one tends to find parameter 'islands' where spinning is possible, while exploration tends to follow 'routes' through this space. Here, we follow two such routes, one of which drastically improves fibre purity, the other changes the nature of the nanotubes comprising the fibres from multiwall to single wall. In the first case there is only a modest enhancement of the mechanical properties, but in the second a very considerable improvement is seen. In terms of the conditions required to make fibres comprising predominately single wall CNTs, the key factor appears to be the rigorous control of the sulphur addition, in trace quantities, coupled with the availability of carbon atoms at the earliest stage after injection, typically in the range 400-500 °C. A model is presented for the role of sulphur in floating catalysts CNT synthesis.