Five months after launching a leveraged buy-out bid of $18.7 billion for Clear Channel Communications, two private equity firms—Bain Capital and Thomas H. Lee Partners—sweetened their offer on Wednesday after two Clear Channel shareholders said they would vote against the deal as originally proposed.

Last year, Clear Channel, the largest radio broadcaster in the U.S. with more than 1,100 stations, put itself up for sale, attracting offers from a host of private equity groups. Although the Clear Channel board eventually accepted the Bain/Thomas H. Lee offer of $37.60 per share plus the assumption of $8 billion in debt, Clear Channel shareholders complained that the price was too low.

Despite efforts to restructure the deal to allay shareholder concerns, opposition continued to grow, inducing the private equity groups to raise their bid to $39 per share.

The improved bid was announced on the eve of a meeting at which two major shareholders—Fidelity Investments and Highfield Capital Management—were expected to vote against the deal. Including the assumption of debt, the revised offer brings the total value of the transaction to $27.6 billion. Accepting the offer, Clear Channel said Wednesday that it would reschedule a vote for May 8 “to allow shareholders time to consider the increase in merger consideration.”