Divertor tokamaks such as ITER also need limiters, namely for startup, rampdown, as well as protection of the main wall from normal and off-normal loads during the diverted phase. In future fusion devices the volume within the magnetic coils will be at a premium and it will be important to make the limiters as thin as possible. A continuous, or almost continuous, wall-limiter can be made thinner than a set of well spaced discrete limiters. The need to be able to remove and replace the components of a wall-limiter requires that its individual panels in fact be discrete but the gaps between the panels should be made as small as possible relative to the panel width to maximize the wall coverage and to minimize the extent of exposed panel edges. The modularity of a wall-limiter leads inevitably to misalignments. The gaps and misalignments reduce the power-handling capability of a modular wall-limiter relative to an ideal wall-limiter, i.e. one without any gaps or misalignments. It is shown that even small gaps and radial misalignments between the individual panels of a modular wall-limiter can require so much shaping, i.e. chamfering, of the panels in order to protect the panel edges that the peak deposited power flux density on the panel face considerably exceeds that for an ideal wall-limiter, typically by an order of magnitude. Nevertheless, compared with a set of discrete limiters which are separated by gaps larger than the limiter toroidal size, a modular, small-gap wall-limiter can still be thinner and can have lower peak deposited power flux densities (MW m−2), for a given total power load (MW).