Three polyethylenes, two Ziegler-Natta linear-low-density materials and one linear polymer, have been crystallized on fibres as linear nuclei to give banded row structures. Whereas the radii of rows of the linear polymer increase linearly with time, those of the two branched polymers do not do so but oscillate around the linear plot in phase with the bands; maximum growth rates occur at the start of both flat-on and edge-on bands. The phenomenon is related to segregation of more-branched molecules which depresses the growth rate. Accelerated growth occurs at the start of the respective bands when lamellae no longer grow parallel but diverge. For edge-on bands this occurs by point-like nucleation and cellulation. Diverging lamellae grow faster than a parallel array because of lower segregant concentration. Accelerated growth may also be correlated with branching because asymmetric branching, with its accompanying increment of lamellar twist, will allow the growth front systematically to reach regions of reduced segregant concentration. A small but repeatable effect in the linear polymer, for which segregation is insignificant and kinetics are not slowed, raises the wider question of whether branching affects growth rate in general.