It has classically been accepted that the healing of narrow wounds in epithelia occurs by formation of a contractile actin cable, while wide wounds are resurfaced by lamellipodial-dependent migration of border cells into the denuded area. To further investigate the general validity of this idea we performed systematic studies of the roles of the wound geometry, wound size and extracellular matrix in wound healing in monolayers of bovine corneal endothelial cells, a system shown here to predominantly display any of the two healing mechanisms according to the experimental conditions. We found that, in this system, it is the absence or presence of the extracellular matrix (ECM) on the wound surface that determines the specific healing mode. Our observations demonstrate that, independently of their size and geometry, wounds created maintaining the ECM heal by migration of cells into the wound area while ECM removal from the wound surface determines the predominant formation of an actin cable. While the latter mechanism is slower, the actin cable permits to maintain the epithelial phenotype to a larger extent during the healing process, as also confirmed by our finding of a more conserved localization of cadherin and vinculin. We also introduce a model that simulates the experimental findings about the dynamics of the healing mechanisms, both for the maintenance or removal of the ECM on the wound surface. The findings of this study may contribute to the understanding of the physiological and pathological aspects of epithelial wound healing and to the design of therapeutic strategies.