The trading of claims in bankruptcy cases fell to $2.1 billion in June, down for the second straight month, as several large companies prepared to exit Chapter 11, according to data released on Tuesday.

Trading has fallen from a record $3.65 billion in April as companies such as Smurfit-Stone Container Corp emerged from bankruptcy, according to data from SecondMarket, which collects the data and runs a bankruptcy claims trading exchange.

It's definitely slowed down a bit, said Chris Moon, director of the bankruptcy claims market for SecondMarket.

He attributed the decline to fewer big cases, as well as the typical summer slowdown.

In the bankruptcy claims market, creditors with claims against companies can trade their interests to investors prior to the conclusion of a bankruptcy case, usually for a steep discount.

The number of claims traded fell to 816 in June from 917 in May, although the number of cases with claims traded rose to 64, the highest this year.

The cases with the most active traded included packaging company Smurfit-Stone, energy company Flying J Inc, chemicals maker Chemtura Corp and media company Tribune Co .

Financial firm Lehman Brothers Holdings Inc , the largest bankruptcy in U.S. history, led the trading of claims as it usually does. Nearly $2 billion of Lehman claims changed hands in 224 trades.

The general trend in the Lehman case is we're hearing a lot of inventory that should be coming to market. Pricing on these claims have pulled back a bit and buyers can be a bit more selective, Moon added.

(Reporting by Tom Hals; editing by Andre Grenon)