The construction of initial-data sets to be used in the simulation of black-hole collisions is studied in the context of the conformal-imaging formalism. An approach is described for evaluating a formal, infinite-series solution of the momentum-constraint equation. This solution allows for the construction of completely general three-dimensional configurations of two black holes with individually specifiable linear and angular momenta. Using this solution for the momentum constraint, the Hamiltonian constraint is solved numerically in the restricted case of axisymmetric configurations. Two codes for solving the Hamiltonian constraint are described, one based on bispherical coordinates and the other on Cadez coordinates. The accuracies of the numerical solutions are gauged by comparison with analytic results, Richardson extrapolation, and comparison of the results from the two codes. Finally, the physical content of data sets representing two equal-sized holes with linear or angular momenta is explored. The results show several expected physical effects including the gravitational spin-spin interaction.
