Access dictionary in order?

[Roy Smith]

I've got a dictionary of items which I will sometimes want random access
to, but sometimes I'll want to be able to step through the items in a
fixed order as well.  Any good way to do that?

The best I've come up with so far is to keep a parallel list of the
dictionary keys in sorted order and use that to step through when I need
to:

   for key in keylist:
      do_stuff (dict[key])

which will work, but seems kind of clumsy.  Anything smoother I can do?