UDS - Offset Smoker Flavor

Do you know if it is possible to get more of an offset smoker flavor from an Ugly Drum Smoker.  I'm talking about more of a Texas smokehouse flavor.  My UDS has only been finished for a few days and I have only done one brisket.  I did notice that the juice and fat dripping onto the charcoals had a pretty strong impact on the flavor.  Not bad, but just different.  I'm wondering it using a drip pan and maybe adding some extra wood might help.  

Any suggestions?

Alan