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Coulomb-explosion velocity-map imaging is a new and potentially universal probe for gas-phase chemical dynamics studies, capable of yielding direct information on (time-evolving) molecular structure. The approach relies on a detailed understanding of the mapping between initial atomic positions within the molecular structure of interest and the final velocities of the fragments formed via Coulomb explosion. Comprehensive on-the-fly ab initio trajectory studies of the Coulomb explosion dynamics are presented for two prototypical small molecules, formyl chloride and cis-1,2-dichloroethene, in order to explore conditions under which reliable structural information can be extracted from fragment velocity-map images. It is shown that, for low parent ion charge states, the mapping from initial atomic positions to final fragment velocities is complex, and very sensitive to the parent ion charge state as well as many other experimental and simulation parameters. For high charge states, however, the mapping is much more straightforward and dominated by Coulombic interactions (moderated, if appropriate, by the requirements of overall spin conservation). This study proposes minimum requirements for the high-charge regime, highlights the need to work in this regime in order to obtain robust structural information from fragment velocity-map images, and suggests how quantitative structural information may be extracted from experimental data.