Apparatus is provided for applying one or more patches to a tubular structure in a body of a patient. The apparatus includes an applicator, which is configured to removably hold the one or more patches, and to place the one or more patches at least partially around the tubular structure. The applicator includes one or more patch supports. Each of the patch supports includes a yielding pad, which is removably coupleable to one of the patches; and a stiff back support structure, to which the yielding pad is fixed. Each of the patch supports is shaped so as to define at least one chamber that itself has a volume of at least 0.5 ml when the patch supports are in respective resting states. Other embodiments are also described.