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Activist investor fund Corvex Management has acquired a 9.9% stake in internet radio company Pandora Media Inc. (NYSE: P). It said in a letter to the company’s management that it wants Pandora “immediately” to explore a sale of the company and “to evaluate the results of a fulsome sales process against other options including the risk-adjusted value of continuing to operate on a standalone basis.”

Needless to say the stock price jumped, up about 8% at one point early Tuesday morning.

Corvex’s letter, signed by managing partner Keith Meister, is a classic example of the iron fist inside the velvet glove:

We are optimistic that the Board of Directors and management share our view that Pandora provides a great product with differentiated features, unique scale and engagement, rich data and targeting abilities, and strong consumer brand awareness. Ongoing share gains from terrestrial radio and the gap between consumer time spent on mobile media and the amount of dollars spent by advertisers on mobile advertising should provide a long runway of secular growth for Pandora’s core internet radio business. We also hope you share some of the frustration of stockholders over the company’s poor absolute stock price performance, stock price underperformance relative to the market, and stock price underperformance relative to industry peers over the last year, two years, three years, and since the company’s initial public offering, respectively.

That is followed by a chart that bleeds red all over the page. The letter goes on:

Despite its many strengths, the company has been unable to date to translate its great product into a great business with an attractive public market valuation.  … Some market participants believe Pandora’s expensive push into adjacent business lines reflects a belated admission that growth in the core ad-supported internet radio business has stalled, while others simply do not trust management to execute on future opportunities in a manner which creates value for shareholders.

Near the end, the letter sums up Pandora’s central problem: “Pandora increasingly competes against some of the largest, most sophisticated and well-capitalized companies in the world, many of whom do not need a music service to be a profitable business in its own right.”

Lots of big-name possibilities come to mind: Liberty Media, AT&T, Verizon (which acquired AOL earlier this year) and even Amazon. It will take a company of that size with a serious commitment to streaming music to make Pandora successful against the likes of Spotify, Apple, Google and Facebook.

Pandora’s stock popped more than 6% last February on chatter then that the company was going to put itself up for sale. That didn’t happen, and now that founder Tim Westergren is back in the CEO chair, a sale of the company may appear even more faintly on the radar screen.

Corvex may push for a sale but a buyer willing to pay some premium of around $3 to $5 a share is not going to be easy to find. The firm’s letter makes Pandora’s problems sound as though they were all due to bad management. It’s hard to argue that management has done its job well, but it may be equally hard to argue that Pandora’s model has the legs Corvex attributes to it.

Pandora stock traded up about 6.4% in the noon hour Tuesday, at $10.62 in a 52-week range of $7.10 to $22.60. The consensus price target on the stock is $13.52.