Abstract: A rolled web of centerflow material, such as paper or non-woven material includes perforation lines separating the material into individual wipes or sheets. Each perforation line comprises a varying perforation profile defined by opposite edge portions and a middle portion having generally the same bond strengths, and intermediate portions between the edge and middle portions having a different bond strength. This perforation profile is effective in reducing dispensing defects, and particularly streaming/roping defects. Alternatively, the perforation line may have stronger edge portions adjacent at lest one weaker middle portion.