Four million Americans with extensive tax preferences are subject to the Alternative Minimum Tax (AMT). By taxing a broad definition of income, the AMT makes it possible to have a tax system that both encourages certain activities with generous tax preferences and maintains a semblance of distributional equity. The same rationale supports the imposition of an Alternative Maximum Tax (AMxT), which would cap tax liabilities of individuals with very few preference items and thereby afford Congress greater flexibility in designing the income tax. The original 1969 AMT proposal included an AMxT; it is difficult to justify imposing one without the other.
Hines, James R., Jr. "Understanding the AMT, and its Unadopted Sibling, the AMxT." K. D. Logue, co-author. J. Legal Analysis 6, no. 2 (2014): 367-408.