Biological systems produce phenotypes that appear to be robust to perturbation by mutations and environmental variation. Prior studies identified genes that, when impaired, reveal previously cryptic genetic variation. This result is typically interpreted as evidence that the disrupted gene normally increases robustness to mutations, as such robustness would allow cryptic variants to accumulate. However, revelation of cryptic genetic variation is not necessarily evidence that a mutationally robust state has been made less robust. Demonstrating a difference in robustness requires comparing the ability of each state (with the gene perturbed or intact) to suppress the effects of new mutations. Previous studies used strains in which the existing genetic variation had been filtered by selection. Here, we use mutation accumulation (MA) lines that have experienced minimal selection, to test the ability of histone H2A.Z (HTZ1) to increase robustness to mutations in the yeast Saccharomyces cerevisiae. HTZ1, a regulator of chromatin structure and gene expression, represents a class of genes implicated in mutational robustness. It had previously been shown to increase robustness of yeast cell morphology to fluctuations in the external or internal microenvironment. We measured morphological variation within and among 79 MA lines with and without HTZ1. Analysis of within-line variation confirms that HTZ1 increases microenvironmental robustness. Analysis of between-line variation shows the morphological effects of eliminating HTZ1 to be highly dependent on the line, which implies that HTZ1 interacts with mutations that have accumulated in the lines. However, lines without HTZ1 are, as a group, not more phenotypically diverse than lines with HTZ1 present. The presence of HTZ1, therefore, does not confer greater robustness to mutations than its absence. Our results provide experimental evidence that revelation of cryptic genetic variation cannot be assumed to be caused by loss of robustness, and therefore force reevaluation of prior claims based on that assumption.