A market-pressured eBay with enough problems of its own said Tuesday that it was going spin off Skype, the mostly free computer-to-computer VoIP software that it paid an over-the-top $2.6 billion for in late 2005 with a $1.5 billion earn-out that dwindled to $500 million, never a popular purchase and never an obvious fit.

It said it will IPO the loser in the first half of next year though why it thinks it can pull it off is unclear.

It said the timing would be based on market conditions – which haven’t been decent in months – and has hired Goldman Sachs to manage the affair.

According to the New York Times Skype’s founders Niklas Zennstrom and Janus Friis reportedly reached out to private equity firms lately in an effort to buy back the operation, but the money that could be raised apparently fell short of the mark.

Apparently eBay couldn’t sell it to anybody else either – at least not for the price it wanted. There’s talk it wants at least $2 billion.

eBay claims Skype is a “great standalone business” with “limited synergies with eBay and PayPal.”

Freed, it said it thought Skype would get the focus and resources it needed to compete and give eBay the chance to focus on its core businesses of e-commerce and online payments.

eBay CEO John Donahoe (pictured) gave Skype the last year to get its act together after installing new management that reportedly improved performance.

Last year Skype produced revenues of $551 million, up 44% year-over-year but only amounting to 6% of eBay’s total revenues, with margins of roughly 22%. Registered users hit 405 million at the end of December, up 47%.

eBay, which took close to a $1.4 billion charge to write the thing off, claims Skype will have revenues of upwards of $1 billion in 2011.

eBay has just sold its StumbleUpon recommendation search engine back to its creators. It bought the thing two years ago for $75 million. It did not disclose the sales price.