Shredding: Worth it?

We tend to end up with a lot of woody waste that's too thick to compost and
too thin to use as wood/stakes. We've now got a small mountain of the stuff
next to the compost heaps, and it's not getting any smaller.

If we shred the stuff (up to 1" in diameter), what can we do with it? We
don't need it as a mulch to suppress weeds as we've covered every flower
bed with plants now. In fact, it would be difficult to apply it.

Can we add it to the compost heaps? Maybe use it on the top of patio pots
to discourage slugs? I'm loath to burn it or just throw it away.

The waste is mostly Ash saplings, Sycamore saplings, and branches from
mature shrubs and fruit trees.

Al.