To date, magnetic-resonance force microscopes employing a magnetic-field gradient source mounted to a microcantilever have suffered from a deleterious dependence of the effective cantilever spring constant on the external magnetic field. A “magnet-on-tip” configuration is introduced in which this dependence has been decreased by at least 200 fold, making it feasible to perform arbitrary-sample micron-scale magnetic resonance force microscopy at very high magnetic field. Alternating-gradient cantilever magnetometry is used to quantify the effect and to prove that the existing model of the tip-field interaction is only qualitatively correct. A model is proposed which quantitatively describes the tip-field interaction in the traditional tip configuration. ©1998 American Institute of Physics.