A lawyer, Edwin J. Jacob, who moved between law firms a number of times before getting his name at the head of the partnership list, appears to have been the main trustee of the Special Accounts.
These accounts were held by the lawyers Webster Sheffield & Christie and mainly Jacob Medinger & Finnegan originally, and later taken over by Shook Hardy & Bacon. Because they were accounts under the control of lawyers, the records could not be accessed during lawsuits by the plaintiffs trying to sue the tobacco companies.
How they operated
In each case, when it was decided among the tobacco company executives that a scientist or academic would be paid surreptitiously, the lawyers would determine the allocation needed from each company according to a formula based on sales, then the payment would be made ... either directly to the scientist him/herself or through another party for further laundering. The companies didn't always contribute to each project -- they exercised their own veto over projects by not contributing.
An example: In the case of Harvard University's Carl C. Seltzer the tobacco companies would send their cheques to Shook Hardy & Bacon, who would then pay a special account held quite separate from the university accounts at the Nutrition Department of the Harvard School of Public Health. Professor Frederick J. Stare, the head of the Nutrition Department had total control over this account, and he would then take a percentage (administration fee!) before paying the balance to Seltzer progressively as a "Honorary Research Assistant" at the HSPH.
A similar system was operated by Peabody Museum when Seltzer was forced to retire from the School of Public Health, and relocated to work out of the premises of the museum, still on the grounds of Harvard ... and still using the Harvard letterhead for his letters. In some cases, the payments were then camouflaged as a grant from the Peabody Museum. See this from the RJ Reynolds file marked"SECRET" and held in the "Shook Hardy Bacon Special Account". []
Very often a research proposal which had been rejected by the scientist-members of the Scientific Advisory Board/s of the various tobacco organizations would be passed to the lawyers, who could see the propaganda value in promoting such work. It would then be put through the system as a "Special Project" and be paid through one of these Special Accounts.
Sometimes the lawyers for the tobacco industry would need payment to a witness, or for a scientist willing to act as a consultant or Whitecoat to also be paid this way. See the lawyers explanation for Special Projects (which were paid via the Special Accounts) 
Special Account #1
Special Account #2
Special Account #3
This account was initially to create a central file of information which would be used by lawyers, Lorillard document files for this account say "LITIGATION RE: TOBACCO LITIGATION FUND(SPECIAL ACCOUNT #3) " Note that the law firm making this arrangment is not the one being paid the cheque.   
The money in this account was non-specific, and was topped up regularly when required. 
The control of this fund appears to have shifted to Shook Hardy & Bacon about 1969. 
Special Account #4
This was the most common account used to pay consultants and witnesses -- mainly university scientists, academics, and the occasional private consultant/company for work done which needed to be kept out of the normal accounts to prevent the possibility of disclosure.
- See this list of Special Project consultants and witnesses and the amount they were paid. 
- Lawyer Alex Holtzman at Philip Morris wants the payment to the Swedish scientist Rune Cederlof to be laundered through a special account before he hands the check over. 
Special Account #5
This appears to have been reserved for behavioral research projects. Richard Brotman and Alfred Freedman did a number of projects for the tobacco industry as a whole, which needed to be paid through these secret accounts. See 
CTR Special Accounts
The Council for Tobacco Research also had Special Projects which were payments that the lawyers determined needed to be conducted surreptitiously. These were paid via Special Accounts and were outside the routine operations of the CTR. See  Only "Tobacco Trustees" qualified for Special Projects.
Horace Kornegay, the ex-Congressman who headed the Tobacco Institute, claimed in his disposition that CTR special projects were only those which fell outside the rule of the CTR, that all research projects needed to be completed within a year. See page 179 
Miscellaneous Special Accounts
- This marks the "dissolution of the Special Account" of Earle Clements in April 1977. Tthis payment is being made to Senator Earle C. Clements who also acted as a tobacco lobbyist in Congress, and was later recruited to head the Tobacco Institute.  He had his own Special Account between 1964 and 1977.