"Rigidities" is not just the problem of Giants. Rigidity is a disease in 3-person accountancies and 11-table restaurants only one year old.
Stop what you are doing.
Call your best customer.
Ask: How are we doing compared to a year ago? Six months ago? Are we making your life more complicated? Are we more bureaucratic in any way, shape, or form? Are we slowing down? Do we ever say, "I'd like to do that for you, but ..."? Etc.
Call your best vendor.
Repeat the above.
Visit your newest employee.
Ask: Have you run across procedures since you got here that you think are silly or over-complicated? If so, have you passed your concerns along? If you haven't, why not—do we make it intimidating to surface such concerns? If you have passed such concerns along, have you been praised for doing so? Has anything happened?
At every Exec Group meeting, set aside a 15-minute block to discuss a "dumbest thing we've done lately" item—insist that members bring a case along for discussion.
There's nothing special about my suggestions here—they are not necessarily meant to be followed, but merely to get you thinking about some anti-rigidity rituals you might invent.