A method of additively manufacturing composite part comprises depositing a segment of a continuous flexible line along a print path. The continuous flexible line comprises a non-resin component and further comprises a photopolymer-resin component that is uncured. The method further comprises delivering a predetermined or actively determined amount of curing energy at least to a portion of the segment of the continuous flexible line at a controlled rate while advancing the continuous flexible line toward the print path and after the segment of the continuous flexible line is deposited along the print path to at least partially cure at least the portion of the segment of the continuous flexible line.