A key challenge in developmental biology is to understand how the collective behaviour of cells gives rise to tissues and structures of reproducible shape across a particular species. Elia Benito-Gutierrez and co-workers now investigate this question by employing single-cell morphometrics to study notochord development, which involves mesodermal progenitors organising themselves into an elongated rod, in the chordate amphioxus. The authors generate a dataset of cell morphologies at different stages of notochord elongation and separate cell shapes by principal component analysis. They demonstrate that the cells in the central notochord undergo two sequential shape transitions that coincide with separate phases of notochord elongation, namely dorsoventral cell intercalation and anterior-posterior (AP) cell elongation. Cell growth underpins AP extension of the notochord, as it prevents loss of AP cell length during intercalation and further increases AP cell length afterwards. The authors show that intercalation proceeds in a bi-directional wave, occurring first in the centre of the notochord and later progressing towards the anterior and posterior tips. However, full notochord elongation also requires cell division of posterior notochord progenitors. Collectively, these findings reveal the principles of notochord morphogenesis in a basally branching chordate and thus provide clues to understanding the evolution of this process in higher vertebrates.