Twitter’s announcement that CEO Dick Costolo is stepping down brought about a mixture of shock and relief on Wall Street. But who will be next to take the helm? Co-founder and former CEO Jack Dorsey is currently serving as interim CEO, and many have suggested that he may end up taking over permanently.

Twitter's Next CEO: Who Will It Be?

But who else might be on Twitter’s short list? SunTrust Robinson Humphrey Robert Peck and his team offered up some suggestions.

Requirements for Twitter’s next CEO

There have been some disagreements among analysts regarding what kind of CEO Twitter needs. Several firms have suggested a product specialist, while others think an engineering or advertiser expert is needed. Peck and his team offered a list of five key things they believe the micro-blogging platform’s search committee is probably looking for.

It should go without saying that the company needs someone who already uses its platform often and is very familiar with it. Second, he said product expertise is required, which again should come as no surprise because this is a requirement that’s been widely talked about.

Third and fourth, he said strong relationships with advertisers and media companies are important, respectively, and fifth, he notes that experience running a large media company is essential as well.

Peck also said it’s important for Twitter to move quickly in selecting its next CEO in order to limit distractions to the company’s attempt to fix its user growth problems.

Internal candidates at Twitter

He named five executives he thinks should be at the top of Twitter’s list of CEO candidates. Of course Dorsey is at the top of the list. In addition to being Twitter’s interim CEO, he’s also chairman of the company CEO of Square. Many people think Dorsey is a “product visionary,” according to Peck, which is important because Twitter has been having so many product issues.

Of course it’s natural to be concerned about whether he could run Twitter at the same time as Square, but many have speculated that he will leave the top post at Square to focus on the CEO position at Twitter.

The other internal candidate at Twitter I Adam Bain, who is currently Twitter’s president of Global Revenue and Partnerships. Peck said his conversations within the industry suggest that Bain is the only internal candidate other than Dorsey. He added that Bain is highly regarded in the industry and already has more than 1,700 directly reporting to him.

In terms of concerns, however, he notes that Bain may not know the product side of Twitter well enough. Also Bain has not been a CEO of a public company, although previously he was a CTO at Fox.

External CEO candidates

Third on Peck’s list is Flipboard co-founder and CEO Mike McCue, who previously was on Twitter’s board and worked at Netscape. The SunTrust analyst said McCue offers “a unique set of skills and respect,” noting that he has plenty of product experience and also strong media and advertising ties. He’s also familiar with Twitter since he served on the company’s board.

The issue with McCue is that many investors think he could only become Twitter’s CEO if the company acquires Flipboard, which Peck estimates could cost as much as $1 billion. However, Flipboard could make a good acquisition for Twitter, so it wouldn’t be all bad.

In fourth place is Scout Chairman and former Yahoo CEO and Fox Interactive President Ross Levinsohn. He has strong media and advertising connections and plenty of CEO experience. Peck thinks Wall Street doesn’t fully appreciate his product expertise because during his time at Sportsline, he built content, product and “creative aspects.” He also has a strong relationship with Bain as the two worked together at News Corp. Further, Levinsohn has a solid track record of identifying and securing top talent.

And finally, Google VP of Display Ad Products Neal Mohan is in fifth place on Peck’s list. In fact, the analyst notes that Mohan’s name was floated by investors as far back as December when there was talk of Costolo resigning.

As of this writing, shares of Twitter were up 3.98% to $36.04 per share.