Only 39% of Fortune 500 CEOs have any social media presence at all – and that’s the good news.

A new study sponsored by Domo and CEO.com has found that top executives at America’s largest firms continue to be slow to adopt the tools that in some cases are being aggressively used by their own marketing departments. The percentage of CEOs with social networking accounts grew from 32 percent last year, but most of the recent adopters are young CEOs who are new in their role. The numbers are gradually ticking up, but only gradually. Seventy percent of Fortune 500 CEOs weren’t active on social media when the first report was published in 2012, compared to 61 percent today.

Not surprisingly, the business-oriented LinkedIn is the social network of choice, with 70 percent of the CEOs who have any social presence maintaining a profile there. Just one in ten of the top executives surveyed have Twitter accounts and only 60 percent have posted within the last 100 days. In other words, the social platform favored by politicians, athletes, actors and other celebrities is almost completely avoided by the business world’s elite.

Of those CEOs who have a presence, most confine their activity to LinkedIn or Twitter. Just 44 CEOs spread their activity across two networks, and just 12 – or 2.4 percent are active on three or more. Notable outliers are Salesforce.com Inc.’s Marc Benioff and Expedia Inc.’s Dara Khosrowshahi, both of whom lead Internet companies. Just two of the 500 maintain personal YouTube channels, although more than 200 are featured on YouTube videos put out by their companies.

The survey would appear to support the perception that Twitter is declining in importance. On average, active CEOs tweet about once every five days, down from once every other day in last year’s study. Seven CEOs have never used their Twitter accounts, including IBM’s Virginia Rometty, who has nearly 16,000 followers despite never having sent a tweet.

Berkshire Hathaway CEO Warren Buffett sparked a Twitter storm when he joined the social network in May, 2013. His first tweet – “Warren is in the house” – was retweeted a record 43,150 times. Yet in the nearly three years since then he has only issued six other messages to his 1.1 million followers.

The survey goes into detail about specific platforms as well as the Twitter follower counts of active CEOs, but the overarching message is that senior executives are avoiding the platforms that put them in the most direct contact with customers, business partners, investors and the media. Numerous studies have documented this phenomenon but none has definitively established a reason for it. Could it be that CEOs fear running afoul of regulators? Are they concerned that social media could become a drag on their time? Is it simple fear of the unknown?

Whatever the reasons, they don’t seem to bother executives like Virgin Group Ltd.’s Richard Branson, who has seven million followers on Twitter and millions more on other social networks. If the CEO of a $20 billion firm can find time to interact with his constituents, what’s holding back the others?