In the imaging genetics field, the classical univariate approach ignores the potential joint effects between genes or the potential covariations between brain regions. In this paper, we propose instead to investigate exploratory multivariate methods, namely partial least squares regression or canonical correlation analysis, in order to identify a set of genetic polymorphisms covarying with a set of neuroimaging phenotypes. However, in high-dimensional settings, such multivariate methods may encounter overfitting issues. Thus, we investigate the use of different strategies of regularization and dimension reduction, combined with PLS or CCA, to face the very high dimensionality of imaging genetics studies. We propose a comparison study of the different strategies on a simulated dataset. We estimate the generalisability of the multivariate association with a cross-validation scheme and assess the capacity of good detection. Univariate selection seems necessary to reduce the dimensionality. However, the best results are obtained by combining univariate filtering and L-1-regularized PLS, which suggests that discovering meaningful genetic associations calls for a multivariate approach.