The isl schedule is based on the Pluto scheduler, which is a successful polyhedral scheduler that is used in one form or another in several research and production compilers. The core scheduler is focused on parallelism and temporal locality and does not directly target spatial locality. Such spatial locality is known to bring performance benefits and has been considered in various forms outside and inside polyhedral compilation. For example, the Pluto compiler has some support for spatial locality, but it is limited to a post-processing step involving only loop interchange. Consecutivity is a special case of spatial locality M that aims for stride-1 accesses, which can be useful for constructing burst accesses and for vectorization. Stride-1 accesses have been targeted by an approach based on one-shot scheduling, but it is fairly approximative and not directly transferable to a Pluto-style scheduler. This report describes an approach for consecutivity that is integrated in a Pluto-style polyhedral scheduler. Both intra-statement and inter-statement consecutivity is considered, taking into account multiple references per statement and the integration into a component based incremental scheduler.