Maximum likelihood estimates are obtained for long data sets of bivariate financial returns using mixing representation of the bivariate (skew) Variance Gamma (VG) and two (skew) "t" distributions. By analysing simulated and real data, issues such as asymptotic lower tail dependence and competitiveness of the three models are illustrated. A brief review of the properties of the models is included. The present paper is a companion to papers in this journal by Demarta & McNeil and Finlay & Seneta. Copyright (c) 2010 The Authors. Journal compilation (c) 2010 International Statistical Institute.