A systematic study of the ground-state binding energies of a hydrogenic impurity in quantum dots subjected to external electric and magnetic fields is presented. The quantum dot is modeled by superposing a lateral parabolic potential and a square-well potential and the energies are calculated via a variational approach within the effective-mass approximation. The interplay between the confinement effects due to the applied fields and the quantum-size confinements on the binding energies is analyzed. The role played by the impurity position along the well direction on the impurity energies is also discussed. We have shown that by changing the strength of the external electric and magnetic fields, a large spread in the range of the donor binding energy may be obtained, for a particular choice for the lateral confinement. The presented results could be used to tailor energy states in optoelectronic devices. ©1997 American Institute of Physics.