This is a used bike, and I'm the third owner.

It has Shimano 105's.

When I try shifting to a smaller cog (by pushing the smaller lever inwards), I have to hold the main lever with my middle finger then shift the smaller lever with my fourth finger.

If I just push the little lever inwards, it will pull the big lever with it, effectively not shifting.

What's wrong? It is a 1999 Raleigh R600, so it's obvious that there could be issues w/ an older bike. (somewhat old)

Thanks