The latest transfer to customers of the defunct brokerage will bring total distributions to $4.1 billion, trustee James Giddens said in a statement today. The transfer, which will rely on CME Group Inc. and clearing organizations for data and assistance, may be completed in two to four weeks, he said.

MF Global customers have been demanding their assets in court filings and letters faxed to the judge handling the case. Giddens previously planned to distribute 60 percent of what should have been in commodity customers’ accounts, saying it would take $1.3 billion to $1.6 billion, or almost all of the assets he had within his control.

Giddens said today that the larger distribution will leave him with enough assets in reserve to deal with any missing customer money.

The shortfall in the MF Global brokerage’s U.S. segregated customer accounts may exceed $1.2 billion, more than double what was previously expected, Giddens has said. That would mean customer accounts are missing about 22 percent of their total of $5.4 billion. A shortfall of 11 percent had been previously estimated by the Commodity Futures Trading Commission.

In its Oct. 31 bankruptcy filing, parent company MF Global Holdings listed debt of $39.7 billion and assets of $41 billion. The firm said it has about $26 million in cash. Corzine, the former co-chief executive officer of Goldman Sachs Group Inc., quit as MF Global’s CEO on Nov. 4.

The brokerage case is Securities Investor Protection Corp. v. MF Global Inc., 11-02790, U.S. District Court, Southern District of New York (Manhattan). The parent’s bankruptcy case is MF Global Holdings Ltd., 11-bk-15059, U.S. Bankruptcy Court, Southern District of New York (Manhattan).