We have used molecular-beam epitaxy (MBE) to grow Co/Pd superlattices along the three high-symmetry crystal axes: [001], [110], and [111]. Identical conditions were maintained for all depositions, and a series of samples of fixed Pd thickness (tPd = 10 ± 1 Å) and varying Co thickness (2 Å ≤ tCo ≤ 22 Å) were prepared for each orientation. A variety of in situ and ex situ characterization studies were made, which confirm these superlattices are single crystalline for all growth directions. The dependence of the uniaxial magnetic anisotropy energy on the Co thickness in these superlattices showed significant systematic differences for each of the three crystal orientations. These variations result entirely from differences in the volume contribution to the anisotropy. Estimates of the magnetocrystalline and magnetoelastic contributions for the (111) and (001) samples are in good agreement with the measured anisotropy energies of these oriented superlattices.