Abstract Multi-agent pathfinding (MAPF) has applications in navigation, robotics, games and planning. Most work on search-based optimal algorithms for MAPF has focused on simple domains with unit cost actions and unit time steps. Although these constraints keep many aspects of the algorithms simple, they also severely limit the domains that can be used. In this paper we introduce a new definition of the MAPF problem for non-unit cost and non-unit time step domains along with new multiagent state successor generation schemes for these domains. Finally, we define an extended version of the increasing cost tree search algorithm (ICTS) for non-unit costs, with two new sub-optimal variants of ICTS: -ICTS and w-ICTS. Our experiments show that higher quality sub-optimal solutions are achievable in domains with finely discretized movement models in no more time than lower-quality, optimal solutions in domains with coarsely discretized movement models.