A classical view of the double-stranded deoxyribose nucleic acid (DNA) as an isotropic elastic rod fails to explain its high flexibility manifested in the formation of sharp loops that are essential in gene regulation and DNA storage. Since the basic structure of DNA can be divided into the external highly polar backbone and the internal hydrophobic bases, here we model DNA as an elastic rod inlaid with fibrils. If the fibrils are much stiffer than the rod, we find that the persistence length of short DNA can be much smaller than that of long DNA with an adapted shear lag analysis. Consequently, the cyclization rate for short DNA is found to be much higher than the previous prediction of the worm-like chain model, which is interestingly in consistency with experiments. Our analysis suggests that the bending of short DNAs can be facilitated if there exists a specific structural heterogeneity.