We have used a computational model to calculate the potential energy surface for dinucleotide steps in double helical DNA as a function of the two principal degrees of freedom, slide and shift. By using a virtual bond to model the constraints imposed by the sugar-phosphate backbone, twist, roll, tilt and rise can be simultaneously optimised for any given values of slide and shift. Thus we have been able to construct complete conformational maps for all step types. For some steps, the maps agree well with experimental data from X-ray crystal structures, but other steps appear to be strongly perturbed by the effects of context (conformational coupling with the neighbouring steps). The optimised values of twist and roll show sequence-dependent variations consistent with the crystal structure data. The conformational maps allow us to construct adiabatic paths, and hence calculate the flexibility of each step with respect to slide and shift. Again the results agree well with the available experimental assignments of flexibility: YR steps, CA/TG and CG, are the most flexible and RR steps, such as AA, the least flexible.