The drive towards greater use of fiber-reinforced composites in primary structures, such as aircraft structures and wind turbines that are increasingly unitized, calls for advanced repair techniques that can restore the structural integrity and geometry. Two such repair techniques are stepped repairs and scarf repairs. Under certain conditions, stepped repairs are easier to perform than scarf repairs, but the step corners may cause high level of stress concentrations negatively affecting the strength of the repair. This paper presents an investigation of the effect of step corners on the fracture behavior of stepped joints under compressive loading, particularly after subjecting it impact damage. Joints featuring different corner radii were tested under compressive loading, and results showed that the impact damage reduced the compressive strength, to marginally below the compression-after-impact strength of composite laminates. The findings reveal that stepped repairs can be designed to rival the performance of scarf repairs, due to the similarity in the inherent stress concentrations at ply terminations in both repair configurations.