We describe a generalization of the ubiquitous Maximum Intensity Projection (MIP) method of volume visualization, the Generalized MIP (GMIP). Briefly, this new technique allows the user to specify a range of intensity values which is used to restrict the values that are actually projected. Whereas the MIP method projects the maximum intensity value along a particular line, the GMIP ignores any intensity values either above or below the specified range, and projects only the maximum intensity value along a particular line that is within the specified range. This new method can be computed quickly and is a conceptually simple extension of the familiar MIP method but provides a great deal of new capabilities. For example, in CT, bone can obscure vasculature in MIP renditions but this effect can be reduced by the GMIP. GMIP also allows rendering soft tissue structures in CT and MRI. We compare and contrast this new method with other well known methods such as surface and volume rendering.