When TG is high the recos are: less sugar! Less bread ans pasta, less wine and alcohol, less sugar added.That means that sugar is transformed very easily in TG a storing molecule of fat by the liver.
Another point is post prandial TG and fast TG.
Post prandial TG is more atherogenic through the trapping in the sub endothelial space of TG rich particles containing an ApoB 48 protein.
And a very recent review on the subject:
J. Borén et al. / Clinica Chimica Acta 431 (2014) 131–142