The Drosophila respiratory system consists of two connected organs, the tracheae and the spiracles. Together they ensure the efficient delivery of air-borne oxygen to all tissues. The posterior spiracles consist internally of the spiracular chamber, an invaginated tube with filtering properties that connects the main tracheal branch to the environment, and externally of the stigmatophore, an extensible epidermal structure that covers the spiracular chamber. The primordia of both components are first specified in the plane of the epidermis and subsequently the spiracular chamber is internalized through the process of invagination accompanied by apical cell constriction. It has become clear that invagination processes do not always or only rely on apical constriction. We show here that in mutants for the src-like kinase Btk29A spiracle cells constrict apically but do not complete invagination, giving rise to shorter spiracular chambers. This defect can be rescued by using different GAL4 drivers to express Btk29A throughout the ectoderm, in cells of posterior segments only, or in the stigmatophore pointing to a non cell-autonomous role for Btk29A. Our analysis suggests that complete invagination of the spiracular chamber requires Btk29A-dependent planar cell rearrangements of adjacent non-invaginating cells of the stigmatophore. These results highlight the complex physical interactions that take place among organ components during morphogenesis, which contribute to their final form and function.