1. The objective of the study was to explore the genetic architecture of blood oxygen saturation (SaO) (an indicator trait, negatively correlated with ascites susceptibility), body weight (Weight) and fleshing score (Flesh, a measure of breast conformation) for 4 meat-type chicken lines reared in commercial conditions. 2. Genetic components, including heritabilities and genetic correlations, were estimated by Restricted Maximum likelihood for these traits measured at 6 weeks of age. 3. Data were collected over eight generations of selection and pedigrees comprised in excess of 130,000 birds. 4. Univariate analyses were performed to allow model definition and to obtain starting values for trivariate analyses. The basic model included a random animal effect and, in further models explored, a maternal environmental effect or a genetic maternal effect or both were fitted. Models were compared using likelihood ratio tests. 5. Estimated heritabilities for SaO ranged from 0.1 to 0.2, and there was no evidence of genetic maternal effects for SaO. The environmental maternal component was significant for one of the populations only. Estimated heritabilities for both Weight and Flesh were between 0.2 and 0.4, and there was evidence of environmental and genetic maternal effects for these traits in all populations. 6. Genetic correlations between SaO and Weight and between SaO and Flesh were low and negative. This suggests that, in principle, genetic selection to simultaneously increase SaO, and therefore decrease ascites susceptibility, and WEight and Flesh could be performed using traditional (marker-free) selection methods. We discuss how a putative interaction between ascites and production traits could jeopardise the success of such methods.