Apparatus is provided for applying one or more patches (50) to a tubular structure (80) in a body of a patient. The apparatus includes an applicator (10), which is configured to removably hold the one or more patches (50), and to place the one or more patches (50) at least partially around the tubular structure (80). The applicator (10) includes one or more patch supports (30). Each of the patch supports (30) includes a yielding pad (36), which is removably coupleable to one of the patches (50) and a stiff back support structure (38), to which the yielding pad (36) is fixed. Each of the patch supports (30) is shaped so as to define at least one chamber (42) that itself has a volume of at least 0.5 ml when the patch supports (30) are in respective resting states. Other embodiments are also described.