New York ? Verizon has won the bidding for MCI Inc. a second time, agreeing to pay $1 billion more for the long-distance telephone company, and yet still considerably less than a rival bid from Qwest.

But investors don’t seem convinced Qwest Communications International Inc. will admit defeat. MCI’s stock shot higher after the $7.64 billion deal was announced, surpassing the $23.50 price per share Verizon Communications Inc. has agreed to pay.

The new agreement increases the amount of cash MCI stockholders would receive for their shares while guaranteeing a minimum value for the Verizon shares that they would get as the balance of the payment.

Qwest, the smallest of the nation’s four big local phone companies, said it would reassess the situation, but reiterated its position that its offer of $8.45 billion, or $26 per share, was superior.

This is the second time MCI has opted for a lower payment from Verizon out of concern about Qwest’s questionable financial health and business prospects.

When MCI’s board accepted Verizon’s original $6.75 billion offer in mid-February, it did so despite having an $8 billion bid on the table from Qwest.