Post-mating courtship displays are often viewed as forms of sexual selection that allow individuals to assess fitness benefits from their mates based on honest signalling. However, display costs are not always easy to identify and quantify. Before each breeding attempt, male Black Wheatears Oenanthe leucura carry tens of heavy stones with the bill to form piles near the nest. The consequent increase of wing loading is considered the key display cost, and stone mass a key signal of male quality. However, males must also cope with neck and bill torques, and with outward-pushing forces that tend to slip stones out of the bill; these effects partly depend on stone morphometry. I evaluated the effects of stone morphometry by comparing stones from two territory types differing in density (thus volume for a given mass), i.e. abandoned houses (less dense) versus rock outcrops (more dense). The comparison included samples of available stones to collect (ground), and stones actually collected by the birds (display). Regardless of territory type, display stones were significantly thinner, and generated higher estimated torques but lower outwardpushing forces, than ground stones of the same mass. On average, display stones were also thicker in abandoned houses than in rock outcrops, but their mass was also significantly lower, which resulted in transport costs being similar between territory types. This suggests that males randomly select the stones that they can handle within the limits of local availability and, in abandoned houses, they have more difficulties in handling the heaviest transportable stones because many of these have too great a volume. This study calls for further experimental research on male performance and the cues that females use to assess the display. A broader conceptual framework is also necessary to address the behavioural and morphological consequences of carrying rigid objects with the bill.