Can I add sawdust and wood shavings to compost?

I put sawdust in my compost bin when i put grass cuttings in, stops it going slimey if i spelt that right, and smelling.

I wouldn't put too much at once, though. It should be well-mixed in and not in layers.

My friend has gerbils and she gives me her shavings which as Clarice says is great for adding in between if you've got lots of grass clippings.