Non‐fullerene acceptors (NFAs) have enabled power conversion efficiencies exceeding 19% in organic solar cells (OSCs). However, the open‐circuit voltage of OSCs remains low relative to their optical gap due to excessive non‐radiative recombination, and this now limits performance. Here, an important aspect of OSC design is considered, namely management of the triplet exciton population formed after non‐geminate charge recombination. By comparing the blends PM6:Y11 and PM6:Y6, it is shown that the greater crystallinity of the NFA domains in PM6:Y11 leads to a higher rate of triplet‐triplet annihilation (TTA). This is attributed to the four times larger ground state dipole moment of Y11 versus Y6, which improves the long range NFA out‐of‐plane ordering. Since TTA converts a fraction of the non‐emissive triplet states into bright singlet states, it has the potential to reduce non‐radiative voltage losses. Through a kinetic analysis of the recombination processes under 1‐Sun illumination, a framework is provided for determining the conditions under which TTA may improve OSC performance. If these could be satisfied, TTA has the potential to reduce non‐radiative voltage losses by up to several tens of millivolts.