If you work in a large company and you want to become humble quickly, check out Stall Points, a fascinating stream of research by the Corporate Executive Board that was recently a cover story for the Harvard Business Review. The research shows that almost all companies hit a point where historical growth rates decelerate. Once the corporate growth engine stalls, it is very hard to restart.

The study involved close to 500 companies that have appeared on the Fortune 100 or international equivalents over the past 50 years. Close to 90 percent of those companies experienced a stall, or “secular reversals in company growth fortunes.” Only 50 percent of companies that stalled were able to grow even moderately over the next decade.

There are many reasons why growth becomes increasingly difficult as a company grows. One challenge is that the hurdle for new initiatives becomes so high that many potential game-changing initiatives never see the light of day.

A few weeks ago I was with a group of senior executives at a Fortune 100 company. We were talking about the strategic objectives of that company’s innovation efforts. One executive said that $1 billion felt like a reasonable target for a generic new growth initiative. Another said, “A billion is nice, but at our size we really need to set the target at $10 billion.”

Mathematically, of course, the executive is right. It got me thinking, though. Only 261 public U.S. companies had $10 billion in revenues last year. How many of the high-flying start-up companies over the last decade reached $10 billion in revenue in 10 years? Well, Google hit $10 billion in its eighth year (2006) and … I think that’s it.

The problem is there aren’t very many $10 billion businesses sitting around. Worse, a $10 billion business doesn’t always look like a $10 billion business in its early days. The only reliable way to create that top-line growth of that magnitude is through relatively large acquisitions, which tend to be at best value neutral.

So what’s a giant to do? One key to success is keeping individual units responsible for growth small enough so they can prioritize opportunities that start relatively modestly. For a long time Hewlett-Packard had a practice of splitting up any division that reached a certain size to minimize bureaucracy and leave the smaller unit free to prioritize relatively small opportunities.

Another key is to set reasonable screens for new growth opportunities. By all means make sure there is a story for why a given opportunity could be a blockbuster success. But leave room for exploration, iteration, and small starts, or it will just be a matter of time before you hit your own stall point.

Do any of you have stories of great ideas that were killed because they weren't "big enough" out of the gates?