In steady swirling flows in closed cylinders, it has been common to observe the transition to spirals of otherwise straight dye streaklines. This occurs in the regions where bubble type breakdown occurs but at a slightly lower Reynolds number. These regions are of particular interest for those seeking to explain the origins of vortex breakdown. The hitherto unexplained occurrence of the spiral streaklines, postulated previously to be due to non-axisymmetry of the flow, is found to be due to small offsets of the dye injection from the central axis. The important implications of this finding are that (i) non-axisymmetry is not a necessary route to bubble-type vortex breakdown, and (ii) that flows displaying spiral streaklines may be still sufficiently axisymmetrical for comparison with numerical and theoretical treatments of the breakdown phenomenon.