Randomized, double-blind, placebo-controlled, parallel-group study design with eleven clinic visits (one screening visit, three lead-in/baseline visits, and seven treatment visits) After a 4-week diet only lead-in period, subjects with a triglyceride (TG) level in the high to very high range and with non-HDL-C level above NCEP ATPIII goals will be randomized to receive either open-label atorvastatin 10 mg per day plus double-blinded Lovaza 4g (4 x 1g capsules) per day OR open-label atorvastatin 10 mg per day plus a double-blinded matching placebo (4 corn oil capsules per day) for 8 weeks After the initial 8-week treatment period, the dose of open-label atorvastatin will be titrated to 20 mg per day (with the Lovaza or matching placebo corn oil doses remaining at 4 capsules per day) for an additional 4 weeks At Week 12, a second open-label titration to 40 mg of open-label atorvastatin per day will be maintained for an additional 4 weeks (again with the Lovaza or matching placebo corn oil doses remaining at 4 capsules per day)