There may still be a chance of clawing back some dough from Bear Stearns.

Investors with former Bear hedge fund managers Ralph Cioffi and Matthew Tannin can hold out hope that they’ll recoup at least some of losses tied to the $1.6 billion collapse of the pair’s mortgage-laden funds.

A judge recently awarded gas chain Racetrac Petroleum Inc, $3.4 million in an arbitration case against the funds. The award is short of the $5 million Racetrac originally invested. The award was made two days before Christmas but was just made public on a Web site maintained by the Financial Industry Regulatory Authority.

A Reuters report notes that the ruling is the first in favor of an investor in the Bear funds since a jury acquitted the Cioffi and Tannin of criminal charges in November.

Federal prosecutors had charged Tannin and Cioffi with lying to some investors about the health of the funds as subprime mortgage markets imploded in the summer of 2007.

At its peak, the fund complex run by the two Bear employees managed more than $30 billion in assets tied to esoteric securities underpinned by risky residential mortgages.

According to reports, a three-member arbitration panel determined that Bear, which was bought by JPMorgan Chase, was negligent — something that federal prosecutors were unable to prove.

Meanwhile, Tannin and Cioffic are still facing separate civil charges by the Securities and Exchange Commission Chair Mary Schapiro, charging that they weren’t forthcoming to investors about the health of the their funds.