Score one for shareholders. The two private equity firms vying to buy Clear Channel Communications have raised their bid under pressure from Clear Channel's shareholders. Bain Capital and Thomas H. Lee Partners are offering $39 per share, or $19.4 billion, about 4 percent more than the previous price. The investors will also assume $8 billion in debt.

Some shareholders had hoped for as much as $40 per share from the two buyers, but Clear Channel board members agreed to the offer on Wednesday. It will be put to a shareholder vote on May 8.

Some of Clear Channel's top institutional holders, including Fidelity, had threatened to oppose the deal on the grounds that the price wasn't right. On Monday, the company's third-largest owner of Clear Channel stock, the California Public Employees' Retirement System, said it would not support the sale at $37.60 per share.

It's still unclear if stockholders will agree to the new offer. "It's not exactly a slam dunk," James Boyle, an analyst with the research firm CL King & Associates, told Reuters. "Both sides will continue to posture, and the soap opera continues and the plot thickens."

This fight between Clear Channel investors and the buyout firms has been building since the first offer was made late last year. The company had already pushed the vote back by a month in the hope of finding common ground. The sale requires approval by two-thirds of shareholders, a condition that the parties have struggled to meet.

This is just one example of the growing opposition from large money managers to the buyout firms gobbling up their portfolio holdings. Private equity firms have been reaping huge returns on investments from taking companies private, turning them around, and taking them public again. Money managers who invest for the long term would prefer to reap that return themselves by holding on to the stock during turnaround periods.