Capital Gains and s 1031 Property Exchange

[Steve Elling]

Here's one for the seasoned investors and tax experts out there. Trying to verify something:

I have a rental property that is fully paid off that we are considering selling. Based on what I've gleaned online, it appears that we CANNOT use the proceeds (it's worth about $100K above our original purchase price) in a 1031 Exchange to pay off the mortgages on a couple of our other, existing rental homes. If we went that route, we'd have to pay capital gains.

So, as I understand it, in order to escape paying 15% in capital-gains taxes on the profit, the proceeds from the sale can only be used to purchase another property of equal or greater value, and only within six months, per 1031 Exchange rules. 

Does that sound accurate, or am I whiffing somehow?