  We obtain, using transfer matrix methods, the distribution function $P(R)$ of
the end-to-end distance, the loop formation probability and force-extension
relations in a model for short double-stranded DNA molecules. Accounting for
the appearance of ``bubbles'', localized regions of enhanced flexibility
associated with the opening of a few base pairs of double-stranded DNA in
thermal equilibrium, leads to dramatic changes in $P(R)$ and unusual
force-extension curves. An analytic formula for the loop formation probability
in the presence of bubbles is proposed. For short {\em heterogeneous} chains,
we demonstrate a strong dependence of loop formation probabilities on sequence,
as seen in recent experiments.
