More than half of the people who quit Twitter would be happy to come back if the service provided better filtering options.

And of those who currently use Twitter, about half check the site multiple times per day.

That level of engagement is second only to Facebook and bodes well for the future growth of the social network — if Twitter’s executives decide to focus on growing the number of users, according to Deutsche Bank, which published an analysis of Twitter’s monthly active user (MAU) trends (pdf). The report is based on a survey of 1,100 people online via SurveyMonkey.

Currently, according to the bank’s report, Twitter is focusing more on engaging users — for example, with the “threaded conversations” timeline that shows @ replies in a string below the original tweet they’re replying to. The result has been that Twitter’s MAU figures have stagnated a bit.

But according to the report, that stagnation is merely a temporary — and easily fixable — problem. Once Twitter decides to focus again on growing its user base, through advertising and various forms of marketing outreach, it should be easy for the service to grow its active users. The high levels of engagement of current users and the readiness of former users to rejoin the service are both promising signs.

But for marketers who want to use Twitter to reach customers, there’s even better news: Everyone has heard of Twitter. A staggering 95 percent of the people surveyed stated that they hear about Twitter once or twice a week, and 62 percent even more frequently than that.

Among people who don’t use Twitter, 80 percent hear about Twitter regularly through television — in fact, TV shows are the most frequent medium through which people hear about it.

“This stat is telling and represents opportunity for Twitter to engage and convert non-users in the future. We believe that events like Ellen Degeneres’ Oscars selfie are likely to continue to happen, and should help bring more MAUs to Twitter over time,” the Deutsche Bank report states.

And, as the bank’s analysis gleefully notes, there’s a lot of untapped potential in Twitter-based advertising. First, there’s the nice synchrony between Twitter and television “Many users seem to think ads are regular content (which is a big positive).”

Second, people who use Twitter prefer to do so through mobile devices and often do it while watching TV. That opens huge possibilities for advertisers and TV broadcasters that can embrace Twitter as a “second screen” experience.

Supporting that point is a second report cited by Barron’s today.

“Not only is Twitter meaningful as a ‘second screen’ to live TV, but in some cases, the number of people tweeting approaches the size of the total TV audience for some shows,” Barrons notes, citing a report by Susquehanna Financial Group‘s Brian Nowack.

If Twitter can address its user growth issue, Deutsche Bank believes, it will have a healthy future ahead of it. DB puts a $65 price target on the stock ($TWTR), which closed at $48.77 today.

“In summary, Twitter remains arguably the best way to play the biggest trend in consumer Internet — mobile — which represents over 70 percent of usage and 80 percent of company revenue,” the report concludes.

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