How to remove all text between the outer parentheses in a string?

When I have a string like this:

s1 = 'stuff(remove_me)'

I can easily remove the parentheses and the text within using

# returns 'stuff'res1 = re.sub(r'\([^)]*\)', '', s1)

as explained here.

But I sometimes encounter nested expressions like this:

s2 = 'stuff(remove(me))'

When I run the command from above, I end up with

'stuff)'

I also tried:

re.sub('\(.*?\)', '', s2)

which gives me the same output.

How can I remove everything within the outer parentheses - including the parentheses themselves - so that I also end up with 'stuff' (which should work for arbitrarily complex expressions)?