You're welcome, Chris.  I learned that from a fellow puppet director in my area, so I can't take the credit!  LOL
Daryl, I also would be interested in "Honeydew's" mouth instructions.  I've always wanted to know how to do that! 
Sara

I've never built a puppet with a mouth like busen honeydew's but I think the trick is to use a very soft and flexible foam for the mouth so that it flexes and stretches as easily as possible.  It's also possible that the head is sculpted from a foam block, or more probably made of latex foam.

Oh goodness the pressure is on......

I don't totally know, just a hunch on how it is done by looking at video's and experience.  Jon you have pretty much the idea.  The mouth plate is made out of foam instead of a stiffer material.  Cut a slit out of the shell of the head and the mouth is pretty shallow because your fingers will need to be right up against the foam head so that you can force the mouth open and close easily.  Of course you need to put straps on the foam mouth plate to gain that control. 

I am not sure if the head is sculpted or if flat foam was used.  It is pretty hard from my experience to carve such a perfect round head......it would challenge the most qualified puppet maker.  I suspect that it is sheet foam glued to make the shape.  They might also use a thinner foam for the mouth area to make it easier to open and close.  I know a lot of speculation.....I will need to make a puppet with a mouth like this and see where I go with it.  At least this may give you more ideas to run with.  I know it isn't latex.....very few....if any Muppets were made from latex. 

Daryl H

I'm not trying to step on your toes, Daryl, so here goes my theories (and possible replication of text I've read elsewhere)

I'm not expert but I believe Bunsen is created the same way Miss Piggy's head is, possibly a latex head (which you could easily pre-create the mouth piece) and then a process called 'flocking' is used to cover it in foam. The process involves statically-charged particles which are they drawn to the head?

I do not take credit for the above. I think I read it from the Muppet Central Puppetry board. It is also possible <tries to remember> that this was done for the early Bunsen and the successors were done with foam block forming. If you check out the Of Muppets and Men book, a puppet builder is in fact seen shaving the foam from a uncoloured (dunno the picture is black and white) foam head of Bunsen, and I am presuming that he made it from a block of foam.

Just my two pennies

I like your diagram lovable puppet pals - I didn't think about using elastic for such things clever

I know the early Muppets were all made of foam either carved from a block or shaped from a sheet.  I did read though that some of the muppets are now made of Latex foam so that they can quickly make several identical puppets.  Whether or not bunsen is one of those I don't know.  And I was speculating regarding how he was made originally.

That being said I am very interested in hearing from anyone who has actually built a puppet with a mouth like his.