DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. While the worm-like chain model provides a good description of small to moderate bending fluctuations, it is expected to break down for large bending. Recent cyclization experiments on strongly-bent shorter molecules indeed suggest enhanced flexibility over and above that expected from the worm-like chain. Here, we use a coarse-grained model of DNA to investigate the subtle thermodynamics of DNA cyclization for molecules ranging from 30 to 210 base pairs. As the molecules get shorter we find increasing deviations between our computed equilibrium j-factor and the classic worm-like chain predictions of Shimada and Yamakawa for a torsionally aligned looped molecule. These deviations are due to sharp kinking, first at nicks, and only subsequently in the body of the duplex. At the shortest lengths, substantial fraying at the ends of duplex domains is the dominant method of relaxation. We also estimate the dynamic j-factor measured in recent FRET experiments. We find that the dynamic j-factor is systematically larger than its equilibrium counterpart - with the deviation larger for shorter molecules - because not all the stress present in the fully cyclized state is present in the transition state. These observations are important for the interpretation of recent cyclization experiments, suggesting that measured anomalously high j-factors may not necessarily indicate non-WLC behavior in the body of duplexes.