Phenotypic heterogeneity describes non-genetic variation that exists between individual cells within isogenic populations. The basis for such heterogeneity is not well understood, but it is evident in a wide range of cellular functions and phenotypes and may be fundamental to the fitness of microorganisms. Here we use a suite of novel assays applied to yeast, to provide an explanation for the classic example of heterogeneous resistance to stress (copper). Cell cycle stage and replicative cell age, but not mitochondrial content, were found to be principal parameters underpinning differential Cu resistance: cell cycle-synchronized cells had relatively uniform Cu resistances, and replicative cell-age profiles differed markedly in sorted Cu-resistant and Cu-sensitive subpopulations. From a range of potential Cu-sensitive mutants, cup1Delta cells lacking Cu-metallothionein, and particularly sod1Delta cells lacking Cu, Zn-superoxide dismutase, exhibited diminished heterogeneity. Furthermore, age-dependent Cu resistance was largely abolished in cup1Delta and sod1Delta cells, whereas cell cycle-dependent Cu resistance was suppressed in sod1Delta cells. Sod1p activity oscillated approximately fivefold during the cell cycle, with peak activity coinciding with peak Cu-resistance. Thus, phenotypic heterogeneity in copper resistance is not stochastic but is driven by the progression of individual cells through the cell cycle and ageing, and is primarily dependent on only Sod1p, out of several gene products that can influence the averaged phenotype. We propose that such heterogeneity provides an important insurance mechanism for organisms; creating subpopulations that are pre-equipped for varied activities as needs may arise (e.g. when faced with stress), but without the permanent metabolic costs of constitutive expression.