Summary. A set of three-dimensional models of the same flattened galaxy with a massive halo show significant variability of the spiral structure they admit. The simplest model shows a two-armed trailing density wave whose amplitude is nearly 50 per cent of the disk and that lasts over 10 rotation periods. As more physically realistic features are added, this wave is replaced by a density wave of 25 per cent amplitude lasting for less than four rotation periods. The final, most realistic model has several bisymmetric waves of some 25 per cent amplitude that live less than 1.5 galactic rotation periods. A common feature of all three models is a trisymmetric density wave that has some 36 per cent amplitude and lasts some 1.5 periods. It does not compare well with the Lin-Shu theory of spiral structure.