sweetcorn and sunflower stems.

Better to build a big composter rather than use a bin for twiggy material. I don't know how much space you have though.

Cut the woody sfuff up with secaturs into little bits and it will still take longer to break down.

It will however be a very high quality compost, apparently.

p.s. and I know I can't spell.

Definitely add to the compost bin - as Jake above says sweetcorn stems are quite easy to chop up with secateurs.  Thick sunflower stems are a little easier to deal with if you split them down the middle end to end with a sharp implement, then try and break them up.