Your tax bracket is the tax on your last dollar earned - not your first dollar.
As someone else mentioned, you get to fill up each bracket as you go up.
There are reasons to keep AGI low - especially if you're running into phase-outs for the child tax credit. Plus, as you earn more, you get a bigger bang for your buck by putting money in tax deductible savings tools.
Being in the 35% tax bracket does not mean you're paying 35% in taxes on all of your dollars. But it can mean that you're getting a 33-35% return (or more, with state taxes) on your deductible retirement contributions/HSA by the mere act of depositing them into your retirement accounts. That's hard to pass up. It's hard to give up that kind of investment return.
You should have accessible emergency savings. Beyond that, if you're worried about tax bracket, then you never give up on tax-advantaged savings until you've filled up that space, because the deduction is too sweet. And if you qualify for a ROTH, it's a no brainer to put money there before taxable investments.