Effects of maxillary advancement on maxillary incisor display in patients with skeletal Class III malocclusion and cleft lip and palate

•The correlation between dental, skeletal, and soft-tissue factors and maxillary tooth display after orthognathics surgery was investigated for patients with skeletal Class III malocclusion and those with cleft lip and palate.•The interaction of the groups with covariates showed no statistical difference.•The horizontal position of A, the vertical position of ANS, and the upper lip length were the most predictable parameters for maxillary tooth exposure.•The findings could guide the planning of the maxillary osteotomy with optimal maxillary tooth display during surgery-first approach.