We use intense few-cycle laser pulses to ionize molecules to the point of Coulomb explosion. We use Coulomb's law or ab initio potentials to reconstruct the molecular structure of D2O and SO2 from the correlated momenta of exploded fragments. For D2O, a light and fast system, we observed about 0.3 Angstrom and 15degrees deviation from the known bond length and bond angle. By simulating the Coulomb explosion for equilibrium geometry, we showed that this deviation is mainly caused by ion motion during ionization. Measuring three-dimensional structure with half bond length resolution is sufficient to observe large-scale rearrangements of small molecules such as isomerization processes.