Recent experiments indicate that double-stranded DNA molecules of approximately 100 base pairs in length have a probability of cyclization which is up to 105 times larger than that expected based on the known bending modulus of the double helix. We argue that for short molecules, formation of a few base pairs of single-stranded DNA can provide a `flexible hinge' that facilitates loop formation. A detailed calculation shows that this mechanism explains the experimental data. Our calculation indicates that the rarely excited bubbles may play an essential role in spontaneous formation of small DNA loops in living cells.