The entropy of tightly bent DNA is investigated in a variety of problems : closure probabilities, hairpin formation, nicked coils, plectonemic supercoiling, all in states with liquid-crystalline order. A new semiclassical method is presented for deriving the Green function of a tightly curved wormlike chain. Precise estimates for the entropy arising from undulations are given for tightly bent DNA in weak, intermediate, and strong nematic fields. A formal statistical mechanical analysis is outlined for hairpins and supercoils. The elongation of closed DNA without twist is computed in strong nematic fields. A scaling theory is given for a liquid crystal of untwisted DNA rings in which nematic order and ring elongation are self-consistently coupled. The elongation of plectonemic supercoils is evaluated for weak and strong nematic fields. The pitch of a cholesteric phase of plectonemic or loose supercoils is shown to be directly related to their writhe.