Meaning: don't care about something (example 1, example 2)
Rewrite 1: don't give a tweetRewrite 2: don't give a bee's buzzRewrite 3: don't give a donkey's brayRewrite 4: don't give a leaf's chance in a galeRewrite 5: don't give a dwarf's wink in a toss 
Comment: The last recast of this cliché is probably more appropriate to "midget tossing," but I like the way the words work together better in this use.
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