A technique to speed up stencil computation is introduced. Computation and data reuse schemes are developed for its application to 1-and 3-dimensional stencils. The approach traverses the data domain fewer times than a state-of-the-art, straightforward iterative stencil implementation would. Performance results are shown for a variety of platforms, exemplifying how it can be straightforwardly applied with existing techniques and frameworks. The technique, named Aggregate Stencil-Loop Iteration (ASLI), works by applying a stencil obtained by the original stencil operator convolved with itself one or more times. This more complex operator creates new opportunities for in-register data reuse and increases the FLOPs-to-load ratio. The total number of FLOPs decreases for 1D but increases for 2D and 3D star-shaped stencils. In both scenarios, speed-up relative to the state-of-the-art is achieved. ASLI is relatively easy to implement and works synergistically with existing methods to optimize stencil computations.