How to tighten wood handles on a set of knives?

I have a set off knives with wooden handles. The metal runs all the way through the wood handle, two strips of wood on either side of the metal. Pretty standard set up.

The wood is held on by brass colored pegs (rivets?) that go through the wood, metal, and the wood piece on the other side.

The knives are close to 20 years old, and the wood handles are a little loose, they move around a bit, independent of the metal. Is there a way to tighten them up?

I suspect the "brass colored pegs" are in fact brass rivets. To tighten them, put a strip of electric tape over them on both sides to protect their surfaces. Then place the knife on a steel surface like an anvil and, using a small hammer, tap each rivet firmly and progressively harder until the wooden pieces no longer move.
- brab

Hello Ken1,
I have a set of steak knives about ten yrs old , and I love them. when the wood handles started to loosen, this is what I did.
I wound a long length of thin cotton string dipped in wood glue, tightly around the wooden handle, starting nearest the blade, and winding it closely round and round to about halfway down the handle. I let it dry and brushed some clear nail varnish over the tightened string to make it waterproof.
That gives it extra grip when using the knives. My friends think it was a clever solution for any loose handles, and I've used the system on my garden hand trowel to give it more of a grip. Its a great way to save old handles.