I will present a uniform account of the meaning of sentences involving exceptions, when these  are made with the prepositions ``but'' and ``except'', such as:

(1)  No one except citizens can vote in today’s election.

(2)  Few countries but China had much chance of sailing to the New World before the Europeans claimed everything.

(3)  Start your pruning by cutting down to the soil all but an odd number of main trunks.

(4)  I asked little except what they had been doing.

All exceptions are licensed by generalizations which can, but need not, be universal; one needs to account for both. The literature on exceptives focuses to a large extent on universal generalizations where a proper name follows the exceptive marker, but these analyses do not generalize correctly to other cases. To obtain adequate truth conditions, one needs to (i) give a plausible story about what generalizations with exceptions mean, and (ii) check a wide variety of examples of how such claims are expressed. We do both in the paper. As far as we can see, our simple account, formalized as the conjunction of a Generality Claim and an Exception Claim, gives correct truth conditions for all the different ways ``but'' and ``except'' are used in exceptives. We also argue that these two prepositions are synonymous, contrary to the widely held view that a difference in meaning between them explains their difference in distribution.