Oh, what a tangled (oily) web we weave: Vice President Dick Cheney's office denied Sunday that he was involved in a coordinated effort to secure a multibillion dollar Iraq oil deal for Halliburton, his former employer. A reference to such an arrangement was made in an internal Pentagon e-mail from an Army Corps of Engineers official to another Pentagon employee, Time magazine reports in its June 7 edition, which is due on newsstands Monday. The existence of the e-mail was confirmed to CNN by a senior administration official familiar with it. The e-mail -- dated March 5, 2003 -- says Douglas Feith, undersecretary of defense for policy, approved the arrangement to award the contract to the oil-services company, the administration official said. According to an e-mail excerpt in Time, the contract was "contingent on informing WH [White House] tomorrow. We anticipate no issues since action has been coordinated w[ith] VP's office." Yes, that's the same Vice President who remained on Halliburton's payroll after entering the White House.