Properties of DNA double helix have been studied for over 60 years. Yet as more sensitive tools become available, fundamental assumptions in our understanding of these properties are being challenged. One such question is over the flexibility of DNA. Looping or bending of DNA on short length scales is essential for many cellular processes but it is highly controversial exactly how flexible the DNA is. Using a new, single-molecule based method, we found that DNA of lengths as short as 50 base pairs can form a circle more than 108 times faster than theoretical predictions. Another question concerns the physical principles governing the reversible, helix-coil transitions of DNA between the double helix and single strands. Using porous nanocontainers, we found that the rate of double helix formation shows an abrupt 100 fold change depending on whether there are 7 or more contiguous base pairs or not.