The concept of robustness in biology has gained much attention recently, but a mechanistic understanding of how genetic networks regulate phenotypic variation has remained elusive. One approach to understand the genetic architecture of variability has been to analyze dispensable gene deletions in model organisms; however, the most important genes cannot be deleted. Here, we have utilized two systems in yeast whereby essential genes have been altered to reduce expression. Using high‐throughput microscopy and image analysis, we have characterized a large number of morphological phenotypes, and their associated variation, for the majority of essential genes in yeast. Our results indicate that phenotypic robustness is more highly dependent upon the expression of essential genes than on the presence of dispensable genes. Morphological robustness appears to be a general property of a genotype that is closely related to pleiotropy. While the fitness profile across a range of expression levels is idiosyncratic to each gene, the global pattern indicates that there is a window in which phenotypic variation can be released before fitness effects are observable.