When the target magnetic structures have clear interfaces and significant petrophysical contrasts to the surrounding strata, the focusing (or sharp-boundary) inversion methods are preferred over the smooth inversion methods. The result of focusing inversions depends on the types of the focusing model constraint (stabilizer). In this study, we propose an adjustable exponential minimum support (AEMS) stabilizer, which is an extension of the previously introduced exponential minimum support (EMS) stabilizer. AEMS is similar to EMS, but it includes an adjustable focusing scheme to control the sharpness of the resulting structure. Using synthetic models, we compared the inversion results obtained with the AEMS method to those obtained by smoothing stabilizers and other focusing stabilizers. AEMS inversion results have a more accurate physical-property distribution and are closer to the true models, indicating an improved model recovery from the other inversion methods. The improvement is mainly attributed to the adjustable scheme of the focusing parameter in the AEMS method. Then, we inverted a field dataset using the AEMS inversion method to obtain a new reference model for copper-gold porphyry deposit detection and interpretation.