The magnetic hyperfine fields of Cd guest atoms in nickel have been measured by perturbed angular correlation spectroscopy with an unprecedented precision. The experiments exhibit the well-known oscillations which have been attributed to the substitutional and the cubic C-site of Cd in nickel, but also show the existence of previously unknown sites through the observation of combined interactions between magnetic hyperfine fields and electric field gradients. The contributions of a large number of possible sites in connection with the properties of the combined interactions are proposed to be responsible for the invisibility of sites as well as for the large amplitudes of some measured frequencies. Following the systematic of magnetic fields of vacancy-associated 5sp-elements in nickel, the measured fields are consistent with theoretical expectations which use the number of vacancies as the primary parameter.