BP is close to capping its busted well in the Gulf for good.

For victims of the three month long oil spill, the process of recovering their losses is only beginning.

Monday, BP announced the company's first $3 billion payment into a $20 billion victims fund.

President Obama appointed prominent attorney Ken Feinberg to oversee the fund.

Feinberg says he will only coordinate the claims for individuals and businesses.

Local governments must still appeal directly to BP for their losses.

'If BP and the White House are saying that while the government claims will come out of the fund, but Feinberg won't handle those claims, you're going to be having more than one hand actually dealing with the fund and will you get inconsistent results, we don't know,' said New Orleans attorney Walter Leger.

Leger represents St. Bernard Parish in the claims process against BP.

'There's a lot of complexity and mostly, there's a lot that we do not know,' he said. 'That's why lawyers are waiting to read the written trust and escrow agreements to see what's involved.'

Jefferson Parish President Steve Theriot says his parish is looking at major ongoing losses from the BP spill.

'We still have issues that we're going to be encountering in terms of a reduction is sales tax, reduction in property tax, reduction in ad valorem tax as we go along,' said Theriot.

Theriot says Feinberg or someone like him should handle claims for local governments as well.

'BP has to be responsible for its shareholders, where Mr. Feinberg or at least a third party administrator would hopefully be representing the claimants who are coming forward with damages to be reimbursed,' said Theriot.

BP plans to tap into the fund to help cover its own expenses during the oil spill response and recovery.

'BP has said that their expenses have totaled between $4 billion and $4.5 billion,' said Leger. 'If BP makes a claim against their own money, then it actually starts off being a $15.5 billion fund or $16 billion fund at best.'

BP is expected to make another $2 billion payment into the victims fund in the fourth quarter of this year.

After that, the company has pledged $5 billion a year for the next three years.

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