It has been established that coarse strip density, air-interspace grid systems can suppress scatter in general radiography and in mammography more effectively than conventional high strip density grids. However, such systems have never gained clinical acceptance due to the large distance the grid needs to move to suppress gridline artifacts and due to their corresponding bulk. We present a novel technique for suppressing grid lines using an x-ray exposure wave form with a soft start and soft stop. The wave form is achieved by varying the x-ray tube current during the exposure. We derive the conditions that the time dependence of the x-ray exposure output needs to meet to suppress gridline artifacts with only a modest grid movement. The technique allows for the design of compact coarse strip density grid systems. We present experimental results that demonstrate the feasibility of the technique.