I might tip this rubbish! (2,3)
I believe the answer is:
my hat
This clue is a double definition.
'i might tip this' is the first definition.
(as in tipping your hat in respect)
'rubbish' is the second definition.
(both are said to show you don't believe something)
(Other definitions for my hat that I've seen before include "I refuse to believe" , "Old-fashioned exclamation" , "Exclamation of surprise" , "nonsense" , "Out of respect I might remove this" .)