Meat quality and carcass characteristics are becoming more relevant for the sheep breeding programs because of their economic value. Understanding the genetic basis for these traits and its relationship with standard traits is necessary for this to be accomplished. Genetic and phenotypic parameters were estimated for 33 growth, carcass and meat quality traits using a large and unique data set from a variety of terminal sire sheep breeds and composites. This is the most comprehensive study to date of genetic parameter estimates for carcass and meat quality traits in New Zealand sheep and includes many traits that are difficult or expensive to measure and novel traits such as number of rib pairs.Heritability estimates ranged from 0.01 for meat redness at 168h after display to 0.44 for ultrasonic eye muscle depth. Most genetic correlations among growth and carcass traits were favourable and moderate to high. However, some genetic antagonisms such as those between carcass fatness and carcass weight were observed indicating that selection to produce heavier carcasses would also result in fatter carcasses. The genetic correlations among meat quality traits were quite variable. Marbling and tenderness were favourably but weakly genetically correlated, indicating that indirect selection gains by selecting only for traditional traits (i.e. growth and carcass traits) would be small and it is recommended that both be included in a breeding program in order to make greater genetic progress in these traits. The genetic correlations among growth/carcass and eating quality traits were moderate to low; however, some genetic antagonisms were observed, such as carcass fatness with marbling and meat redness, indicating that a stronger emphasis on selection for leanness could affect meat quality traits and consequently consumer eating satisfaction.The heritability estimates and phenotypic variances for the carcass and meat quality traits of New Zealand sheep populations suggest that most traits, apart from pH and meat yellowness, have sufficient phenotypic and genetic variation to enable substantial genetic gains to be achieved through selection. The genetic parameters presented in this study provide a valuable reference to design and/or update a terminal sire breeding program emphasizing meat quality traits. It is important to note that unfavourable genetic correlations identified in this study were low to moderate in magnitude, making it practical to select for favourable genetic progress in all traits or at least to maintain commercially acceptable levels for some traits, if they are measured and balanced in a selection index.