Private-equity firms are sitting on more than $1 trillion in uninvested capital, which they will need to spend if they want to earn the hefty fees they collect on investment gains. Their problem: The most efficient way to put the money to work is on big deals, but the raft of failures of precrisis buyouts shows how hard that is to do.

“What we’re in is a situation where you leave no stone unturned in terms of trying to find your next deal,” said Brenda Rainey, a global practice director with Bain & Company.