Potential-field sharp-boundary inversion will allow us to identify the sharp petrophysical deposit boundaries inside the host rocks. With the purpose to find a more simple and convenient way to achieve a sharp-boundary and well-focused image for 3D focusing inversion, we analyze and discuss the influence of the focusing parameter in several commonly used stabilizing functionals, such as minimum support (MS), minimum gradient support (MGS), modified total variation (TV) stabilizing functional, etc. Then, we evaluate an adjustable exponential stabilizing (AES) functional, the focus of which is adjustable by the base and the exponent of the exponential functional, and we apply it to 3D density and magnetic susceptibility inversion for synthetic and field data. Compared with MS, MGS, TV, and other stabilizers, the proposed stabilizer can generate well-focused images and provide sharp boundaries. We also determine that sharp-boundary images produced by the proposed AES stabilizer have a weak dependence on the focusing parameter. Furthermore, we can obtain a stable and focused result by controlling the focusing parameter in the exponent of AES adaptively increasing with the iterations. The model tests and inversion of field data verify the flexibility and stability of this adjustable stabilizer.