Uniformity can significantly impact productivity and profitability of commercial oyster production. For instance, grading management activities (maintaining oysters of similar size to be cultivated together) correspond to one of the main variable costs for oyster growers. Different strategies can be adopted to increase uniformity. If genetic variation for uniformity of a given trait exists, it could be efficiently improved by selective breeding. In the present study, we investigated the existence of genetic variation on uniformity of different production traits in oysters, by modelling the genetic heterogeneity of residual variance, also referred as micro-environmental sensitivity. To avoid misleading inference due to eventual problems related with data structure or statistical artefacts from certain analysis, genetic heterogeneity of residual variance was assessed for two different oyster species, three different traits, and using two statistical methods. The analysed traits were harvest weight, shell length and width index (width to length ratio). The phenotypic measurements came from the ASI Pacific Oyster and the Sydney Rock Oyster Australian breeding populations. The analyses for each trait and dataset used information of approximately 50,000 oysters from about 1,000 families. The statistical methods adopted were the two-step REML and the double hierarchical generalized linear model, both applied under a sire-dam model. The genetic parameters used to assess the feasibility of selection for uniformity were: the genetic coefficient of variation of residual variance (GCVE), also referred as ‘evolvability’, which provides the potential response to selection for residual variance; the heritability of residual variance, used to determine the accuracy of prediction of breeding values for the residual variance; and the genetic correlation between mean and variability. The results showed compelling evidence of genetic control of variability for the different traits, species/datasets and statistical methods evaluated. Evolvability estimates (0.109-0.499) indicated great opportunity to select oysters for uniformity of production, in agreement with estimates from other aquaculture and livestock species. The GCVE estimate of 0.499, for example, indicates that for every change of one standard deviation of the additive genetic variance (of variability), the residual variance is expected to be reduced by 49.9%. The heritability estimates of residual variances were low (0.001-0.025) highlighting the necessity of large progeny size to accurately predict the breeding values for variability or, alternatively, the necessity to implement genomic selection to increase accuracy of prediction. The genetic correlation estimates between the mean and the residual variance were positive and, in general, moderate to high (0.133-0.729) indicating difficulty to simultaneously increase the mean and reduce variability, although some families with this pattern were observed. In summary, the results supported the existence of genetic control of variability for different production traits in oysters, revealing the potential to improve uniformity of oyster production through selective breeding.