Two simple models are used to estimate the electrostatic contributions to the stiffness of short DNA fragments. The first model views DNA as two strands that are appropriately parametrized and are wrapped helically around a straight cylinder radius equal to the radius of the DNA molecule. The potential energy of the DNA due to phosphate-phosphate electrostatic interactions is evaluated assuming that the charges interact through Debye-Huckel potentials. This potential energy is compared with the potential energy as computed using our second model in which DNA is viewed as two helical strands wrapping around a curved tube whose cross-section is a disk of radius equal to the radius of the DNA. We find that the electrostatic persistence length for B-DNA molecules in the range of 105-130 bp is 125.64 angstrom (37 bp) and 76.05 angstrom (23 bp) at 5 and 10 mM monovalent salt concentration, respectively. If the condensed fraction theta is taken to be 0.715 at 10 mM, then the electrostatic persistence length is 108.28 angstrom (32 bp), while that based on taking into account end effects is 72.87 angstrom (21 bp). At 5 mM monovalent salt, the total persistence length for DNA fragments in this length range is approximately 575.64 angstrom (171 bp), using the best estimate for nonelectrostatic contribution to persistence length. Electrostatic effects thus contribute 21.8% to DNA stiffness at 5 mM for fragments between 105- to 130-bp. In contrast, electrostatics are calculated to make a negligible contribution to the DNA persistence length at physiological monovalent cation concentration. The results are compared with counterion condensation models and experimental data.