The growth kinetics and morphology of polyethylene single crystals of a narrow molecular mass fraction (M_w= 1.36 × 10⁴ and M_w/M_n= 1.19) have been studied. Single crystals extracted from the melt show two types of curved lateral habit: a lenticular shape elongated in the direction of the b-axis and a truncated lozenge with curved edges of the {100} growth faces. The change in the lateral habits occurs in the vicinity of a transition in the supercooling dependence of growth rate, which has been explained as a change of growth mode from mono-nucleation (regime I) to multi-nucleation (regime II) growth. It has been argued that the growth mode change can be explained as the result of the morphological change in lateral habits. Concerning the origin of the curved lateral habits, the necessary conditions, such as the slow propagation of steps, have been discussed and a theoretical approach based on Seto and Frank's kinetics has been undertaken. The experimental results obtained are very similar to the results obtained recently for a higher molecular weight fraction and hence the present results confirm the model presented previously.