Beaming question

[Steve Dunlop]

4/4 time.  Lilypond 2.11.33.

I'm trying to get the autobeaming behavior to match an existing style
where:

* Up to four eighth notes can be beamed together (subject to the usual
limitations on ending beat)
* But, when sixteen notes share the beam with eighth notes, beams may
not cross beats.  Another way of saying this is that a beam can only
have one eighth note and two sixteenth notes.

Perhaps an example will make it clear.  I want the autobeamer to make
this:

{ a8 a a a  a a a a16 a }

to look like this:

{ a8 [a a a] a [a] a a16 a }

Can someone help me out?

Thanks

Steve