The genetic improvement of disease resistance and heat tolerance could contribute to the enhancement of health and welfare in the sheep industry. This thesis focuses on gastrointestinal parasite resistance, genetic resistance to scrapie, and heat tolerance in sheep. There are different methods to measure Fecal egg count (FEC), which may be inconsistent. Not accounting for inconsistencies is problematic when integrating data from different FEC methods for genetic evaluation. Data from two FEC methods, the "Modified McMaster" and the "Triple Chamber McMaster", were compared. The differences in FEC means and variances were significant, making the methods incompatible for direct integration as a single trait. Analysis of FEC from the two methods as separate traits showed high genetic correlation. Thus, FEC data from the two methods were integrated, after adjustment for the means and variances, prior to multivariate analysis with indicator traits, which included FAMACHA©, body condition score, and bodyweight. The genetic correlations between FEC and the indicator traits were low, suggesting that including those traits with FEC in a multiple-trait model would not offer considerable advantage. Selection based on scrapie genotype could improve scrapie resistance in sheep. However, few animals are genotyped, resulting in limited gain. Numeric values for scrapie resistance (SR) genotypes were defined from the most vulnerable (0) to the most resistant (4) and then, adjusted to a non-additive genetic effect. Subsequently, an animal model was used to predict SR in non-genotyped animals. The accuracy for prediction ranged from moderate to high, with selection increasing SR of non-genotyped animals. Therefore, the animal model makes better use of available information that could be useful for breeding programs for scrapie resistance in sheep. Heat stress can negatively affect the growth performance of lambs. Temperature-Humidity Index (THI) above comfort zone was used as the environmental gradient for heat stress to examine genotype by environment interaction in growth traits, using a reaction norm model. A genetic antagonism between growth traits and heat tolerance was found and it should be accounted for in breeding programs. Variation in heritability estimates across the heat stress gradient provides opportunity for selection for growth traits within specific environments.