Cleft lip and palate (CL/P), as is true of many craniofacial malformations in humans, is etiologically complex and highly variable in expression. A/WySn mice are an intriguing model for human CL/P because they develop this dysmorphology with a variable expression pattern, incomplete penetrance and frequent unilateral expression on a homogeneous genetic background. The developmental basis for this variation in expression is unknown, but of great significance for understanding such expression patterns in humans. As a step towards this goal, this study used three-dimensional geometric morphometric and novel high throughput morphometric techniques based on three-dimensional computed microtomography of mouse embryos to analyze craniofacial shape variation during primary palate formation. Our analysis confirmed previous findings based on two-dimensional analyses that the midface in A/WySn embryos, and the maxillary prominence in particular, is relatively reduced in size and appears to be developmentally delayed. In addition, we find that shape variance is increased in A/WySn embryos during primary palate formation compared to both C57BL/6J mice and the F1 crosses between these strains. If the reduction in midfacial growth caused by the Wnt9b hypomorphic mutation pushes A/WySn mice closer on average to the threshold for cleft lip formation, the elevated shape variance may explain why some, but not all, embryos develop the dysmorphology in a genetically homogeneous inbred line of mice.