Buying with cash, then get a loan. Is the interest deductible?

[Jim P.]

I'm considering buying an investment property with cash (such as foreclosures that are only available to cash buyers).  I have the cash for it, but I would like to later get a mortgage on it so I don't have so much cash tied up in it.  But if I do that, would the mortgage interest be deductible from my rental income?

Here's another twist. The cash I have right now came from doing a cash-out refi of another completely paid off rental property I have. If I take that cash and buy a property with it, is the interest on that cash-out refi deductible from my rental income for either property? So far these are all just in my own name, not with an LLC by the way.