Sprint Nextel appears to be scrounging for every new customer it can find.

The nation’s third-largest wireless company upped the bounty it pays to Virgin Mobile for each subscriber it adds between October 1 and the end of the year. Sprint also agreed to drop Virgin’s minimum required payments.

This news arrived today in documents Virgin Mobile filed with the Securities and Exchange Commission.

Virgin Mobile was born back in 2002 after Sprint got together with Richard Branson’s Virgin Group to create a new service catering in particular to the youth market.

The company calls itself a wireless communications provider "offering prepaid, or pay-as-you-go, and, following the acquisition of Helio LLC, postpaid services targeted at the youth market."

Virgin sells its own brand of wireless service, but the calls, text messages and other communication bits actually travel over Sprint’s network. Virgin pays Sprint for the use of the network.

Some other wireless companies have similar wholesale relationships set up, but few, if any, have relied on this approach as much as Sprint has.

At the end of September, Virgin had 5.2 million customers. Sprint relied on these subscribers to keep its overall base of customers above – just barely – the 50 million mark.

Virgin previously agreed to pay Sprint at least $320 million for wireless network services in 2008, $370 million in 2009 and $420 million in 2010.

Sprint previously agreed to pay Virgin $2.50 – in the form of a network usage credit up to a total of $10 million – for each subscriber the company added between July 1, 2008 and Dec. 31, 2009.

This week Sprint and Virgin changed their relationship again.

Sprint will provide Virgin with an additional $2 credit for each customer – referred to as a gross addition – that the company signs between Oct. 1 and Dec. 31.

The required payment for 2008 will drop to $318 million. Starting next year, Virgin no longer will be subject to minimum payments and will pay fixed rates for voice, messaging and data traffic it sends over Sprint’s network.

So how much is a Virgin customer worth?

This is a rough calculation, to be sure, but it takes about 11 Virgin customers to equal one of Sprint’s calling contract subscribers paying, on average, $56 a month.

If Virgin pays Sprint $318 million and has about 5 million subscribers, that translates to about $5 per month per Virgin customer for Sprint – before Sprint pays any “network usage credit” bounties for new customers.

Sprint lost another 1.3 million subscribers overall in the third quarter. Many expect the difficult times to continue.

T-Mobile, the nation’s No. 4 wireless carrier, has been growing. It had about 32.1 million subscribers at the end of the third quarter.