Read the mission statements of 100 companies and at least 75 will mention simplicity, says Ron Ashkenas, senior partner at Schaffer Consulting. "We've talked about it for thousands of years. Leonardo da Vinci talked about it, the ancient Greeks talked about it," he says. "But doing it is another thing."

First, CIOs must enlist supporters with pocketbooks, says Ashkenas, who wrote the book Simply Effective: How to Cut through Complexity in Your Organization and Get Things Done.

You might appeal to their sense of doom, or as Begley puts it, to "what matters." For the CEO, it's missing new business because the company is freighted with plodding, confusing technology that costs too much to maintain. For the board of directors, it's managing a crisis after a is traced to vulnerabilities in systems that aren't fully understood.

When Begley described her simplicity plans to GE's board, she explained that a simpler infrastructure is more secure and easier to protect. "When we have incidents, typically, the root cause is some type of complexity," she says. "Cybersecurity is something our board cares a lot about. Our company's reputation is at stake."