Fred B. Brown (Baltimore) has published Reforming the Branch Profits Tax to Advance Neutrality, 25 Va. Tax Rev. 1219 (2006).  Here is the Conclusion:

The branch profits tax is founded on the policy of tax neutrality with respect to the form of conducting a business, yet as currently implemented the provision does not adequately advance this concept. This article proposes several changes to the branch profits tax that both promote neutrality and are consistent with other recognized policies governing the taxation of U.S. branches of foreign corporations. Specifically, I recommend the following reforms: (i) eliminate the potential for recapture upon the termination of a U.S. branch where a foreign corporation elects to reduce its U.S. liabilities, (ii) remove the U.S. booked liability limitation under the election to reduce U.S. liabilities, and (iii) provide foreign corporations with an election to treat investments generating U.S. source income as effectively connected assets. [FN326] With these changes, foreign corporations with U.S. branches generally would have a choice of whether to incur a second-level tax or instead have (or continue to have) the income on invested earnings taxed by the United States on a net basis. Thus, the branch profits tax would function more like the dividend tax in the U.S. subsidiary setting, thereby promoting the neutrality goals underlying the provision.