Matrix-generator and Monte Carlo methods have been employed to study the influence of thermal fluctuations on the overall sizes and shapes of curved pieces of DNA. The DNA model involves the independent angular parameters relating successive base-pair steps: the sequence-dependent equilibrium values and fluctuations of the twist, tilt, and roll angles. The curved sequence under study is the (A5X5)n repeating polymer, the AA and XX steps having different equilibrium roll and twist values. Both planar circles and superhelices are analysed. Detailed comparison is made between the rigorous statistical mechanical representation of the DNA and simplified static models currently used in the literature. That is, a more realistic "flexible wedge" model is contrasted with the existing "static wedge" model of DNA curvature, which is demonstrated to be inadequate. The size of the coils is described by the unperturbed root-mean-square end-to-end distance and the shape by a ratio of the principal moments of the radius of gyration. The moment ratios indicate that when DNA is relatively short (e.g. its length is shorter than half a turn of the static superhelix), the flexible chains are more "short and thick" than the static structure. The end-to-end distances, however, are practically the same in the two models. For longer DNA fragments, the flexible chain is more extended in terms of the end-to-end distance and more globular in terms of the moment ratio. Thus, fluctuations "blur" the curvature of longer DNA fragments compared with static models. Furthermore, the overall average shape of slightly curved DNA subject to natural bending and twisting fluctuations is essentially indistinguishable from that of the corresponding "straight" DNA. Such configurational similarities are apparently responsible for the relative insensitivity of the polyacrylamide gel matrix to small degrees of DNA curvature. These findings raise serious questions regarding the quantitative estimation of wedge angles in DNA from electrophoretic experiments, based on static models. Comparison between planar circles and superhelices shows that when fluctuations are considered, the flexible circles are more spherical than the superhelices. The results imply that when DNA bending is exactly "in phase" with the helical repeat (i.e. when the DNA loop is exactly planar at 0 K), the DNA coil is packed more tightly than when bending and twisting are "out of phase" (and a superhelix is formed at 0 K). This finding is consistent with polyacrylamide gel electrophoresis data testifying to an increase in DNA retardation when twisting is more precisely "tuned".(ABSTRACT TRUNCATED AT 400 WORDS)