Methods to increase the percent of polyunsaturated fatty acids (PUFAs) within the total lipids and oils of PUFA-producing oleaginous organisms are provided herein, by regulating the activity of specific acyltransferases. Specifically, since oil biosynthesis is expected to compete with polyunsaturation during oleaginy, it is possible to reduce or inactivate the activity of an organism's DAG ATs (e.g., phospholipid:diacylglycerol acyltransferase (PDAT) and/or diacylglycerol acyltransferase 1 (DGAT1) and/or diacylglycerol acyltransferase 2 (DGAT2)) to thereby reduce the overall rate of oil biosynthesis while concomitantly increasing the percent of PUFAs that are incorporated into the lipid and oil fractions. The teachings herein will thereby enable one to engineer a wide variety of oleaginous organisms to produce oils with very specific fatty acid compositions.