Four performance-related traits [growth trait (GROW), feed efficiency trait 1 (FE1) and trait 2 (FE2), and dissection trait (DT)] and 4 categorical traits [mortality (MORT) and 3 disorder traits (DIS1, DIS2, and DIS3)] were analyzed using linear and threshold single- and multi-trait models. Field data included 186,596 records of commercial broilers from Cobb-Vantress, Inc. Average-information restricted maximum likelihood and Gibbs sampling-based methods were used to obtain estimates of the (co)variance components, heritabilities, and genetic correlations in a traditional approach using best linear unbiased prediction (BLUP). The ability to predict future breeding values (measured as realized accuracy) was checked in the last generation when traditional BLUP and single-step genomic BLUP were used. Heritability estimates for GROW, FE1, and FE2 in single- and multi-trait models were similar and moderate (0.22 to 0.26) but high for DT (0.48 to 0.50). For MORT, DIS1, and DIS2, heritabilities were 0.13, 0.24, and 0.34, respectively. Estimates from single- and multi-trait models were also very similar. However, heritability for DIS3 was higher from the single-trait threshold model than for the multi-trait linear-threshold model (0.29 vs. 0.19). Genetic correlations between growth traits and MORT were weak, except for maternal GROW, which had a moderate negative correlation (-0.50) with MORT. The genetic correlation between MORT and DIS1 was strong and positive (0.77). Feed efficiency 1, which was moderately heritable (0.25) and is highly selected for, was not genetically related to MORT of broilers and other disorders. Broiler MORT also had moderate heritability (0.13), which suggests that MORT and FE1 can be improved through selection without negatively impacting other important traits. Selection of heavier maternal GROW also may decrease offspring MORT.