How about flat rate, no deductions and the ONLY thing congress is allowed to adjust is the bar. The bar being the agreed upon poverty level.

So, two options here for a $20K poverty level:

$100K = $10K tax.
$20K = $0 tax

or

$100K = ($80K * 10%) = $8K tax
$20K = $0 tax.

So the poor aren't harmed and all that's left is to decide the percentage for everyone else.