Barbarian Expansion:siege towers invunerable?

As the Eastern Roman Empire I'm having a hard time destroying enemy siege towers before they reach my city walls,even with 6 eastern archers with fire arrows shooting them,the things seem to be invunerable to fire of any kind,but I can burn down rams and sap under concentrated archer fire easily enough. Are the things that hard to take down fire archers in fire arrow mode,and if so,what's the best method of dealing with them,as it's frustrating to stop a gothic ram at my gate,only to have them flood the wall with Gothic Spearmen and take the city that way,even though I promptly hired all the mercs in the area and re-took the city from them,as they didn't leave a proper garrison.

If you time it right, one unit of cavalry can charge out and set fire to the siege tower and then escape back to the safety of your walls before the AI can react. Of course the best tactic is to stop the hordes at bridges and slaughter them before they get to your city walls. I annihilated three Hun stacks in one turn.