How to remove unwanted material assigned to surface?

[stealth94rt2]

I am tagging the surfaces of a model with various materials. However, I've noticed that some parts of the model have multiple materials assigned, like this...

I assume the highlighted one is the material actually selected and shown in the editor and rendering. However, I don't see any way of removing the unwanted/extra ones. (There is no "trash can" icon or other means of deleting.)

I would like to clean up my model so I have only one material showing for each surface or part. Please advise on how to do that.

Thanks!

[Ussnorway]

yes but you can select the entire model and give it a new material to replace all the parts

[stealth94rt2]

I'm not sure I understand. I have already gone through my entire model and tagged each surface with the desired material. However, for some surfaces, there is more than one material showing up -- those are what I want to fix.