Bt

On the contrary, rather (as a regular adversative conjunction, introducing a word or clause in contrast or contradiction with the preceding negative clause or sentence).

"I am not rich but [I am] poor  not John but Peter went there."

However, although, nevertheless, on the other hand (introducing a clause contrary to prior belief or in contrast with the preceding clause or sentence).

"She is very old but still attractive."

Except that (introducing a subordinate clause which qualifies a negative statement); also, with omission of the subject of the subordinate clause, acting as a negative relative, "except one that", "except such that".

"I cannot but feel offended."

Without its also being the case that; unless that (introducing a necessary concomitant).

"It never rains but it pours."