Fired Groupon (NASDAQ: GRPN [FREE Stock Trend Analysis]) CEO and co-founder, Andrew Mason has been replaced by Executive Chairman Eric Lefkofsky and Vice Chairman Ted Leonsisa, who will serve as co-CEOs, pending a search for a permanent replacement.

Now the serious work of picking a successor begins, but it’s not the only serious work to be done at Groupon.

In his farewell memo, according to the Wall Street Journal, Mason joked that he planned to shed a few pounds, saying, “FYI I’m looking for a good fat camp to lose my Groupon 40.”

The consensus seems to be that Groupon could use a little slimming down as well. Reuters reports that analysts and investors alike say the company needs to reduce its international arm, creating a more focused, more serious business with a smaller editorial staff.

Groupon would be more profitable if it cut its 10 percent or 20 percent worst performing markets, Jordan Rohan, an analyst at Stifel Nicolaus, said during a Wednesday conference call following the quarterly results.

Groupon is really in three businesses today, says Business Insider: the original daily coupon deal business, a local-commerce business and Groupon Goods, a booming, but low margin, e-commerce business.

Choosing the right person to manage and grow this three-legged business model will be a challenge for Groupon. 

One intriguing potential CEO candidate, according to Business Insider, is Sebastian Gunningham, Amazon's senior vice president of seller services.

BI reports that Gunningham served as CEO of Peace Software and has worked at both Oracle and Apple – providing him with first class credentials as far as Wall Street is concerned.

Other names making the water cooler rumor mill discussion group list include former Yahoo Inc. (NASDAQ: YHOO) CEO, Terry Semel, ex-OpenTable Inc. (NASDAQ: OPEN) CEO, Jeff Jordan, Coinstar (NASDAQ: CSTR) subsidiary, Redbox founder Gregg Kaplan, and Jason Kilar, one-time CEO at Hulu, part of the Comcast (NASDAQ: CMCSA) owned, NBC Universal group.

According to Crain’s Chicago Business, the most important factor in choosing a new CEO will have to do with how Groupon's board views the company. If Groupon leadership decides, as some believe they have, that Groupon Goods is the future, the decision arrow will tilt in one direction. If it decides to stick with the tried-and-true original core business model, that could change everything.

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