Due to decreasing costs of sequencing and genotyping, genome-wide association studies (GWAS) are becoming a standard approach for studying the genetics of natural variation. A major problem in such studies is the complicated dependencestructure of the data. Mixed models have emerged as a general and flexible approach for dealing with this problem. Here we extend this approach to handle correlated phenotypes by deriving a fully parameterized multi-trait mixed model (MTMM) that considers simultaneously both the within- and between-trait variance components for multiple traits. Phenotypic correlation can be due to either a common genetic architecture (pleiotropy) or to a common environmental effect. Dissecting these different causes is of interest not only because of the importance of understanding pleiotropy, but also because we may expect increased power compared to marginal analyses. To illustrate the utility of the MTMM for traits that are correlated, we reanalyzed data obtained for a set of geographically diverse ecotypes, which were grown in replicated common garden experiments in four European field sites. This data have been used successfully before to access the genetic basis for local adaptation and contain both: data for multiple phenotypes measured in the same environment, and measurements of the same phenotypes in different environments. Here we show how the genetic and environmental contribution to a specific trait can be assessed through the use of MTMM. Additionally we report newly associated markers improving our global understanding of both genetic and environmental variation on life-history traits.