Help!

I have a lovely Draceana in a pot on the kitchen windowsill (it's
quite a big windowsill) and the plant has three branches of the main
stem. It's quite big now - around two feet or so high, but recently
the end third or so of each leaf has gone brown, curled up and died.
There are a lot of leaves and it now looks very sad indeed.

Can I revive it at all? Is it worth cutting the dead ends off or will
that make it worse?

Hate to lose it so thanks in advance for any help.

Andy.