The flexibility of short DNA fragments is studied by a Hamiltonian model which treats the inter-strand and intra-strand forces at the level of the base pair. The elastic response of a set of homogeneous helices to externally applied forces is obtained by computing the average bending angles between adjacent base pairs along the molecular axis. The ensemble averages are performed over a room temperature equilibrium distribution of base pair separations and bending fluctuations. The analysis of the end-to-end distances and persistence lengths shows that even short sequences with less than 100 base pairs maintain a significant bendability ascribed to thermal fluctuational effects and kinks with large bending angles. The discrepancies between the outcomes of the discrete model and those of the worm-like-chain model are examined pointing out the inadequacy of the latter on short length scales.