I'll readily admit that I've been leery in the past of stocks with really high dividend yields. And in most cases, I still am. When a dividend yield is in the stratosphere, there's often a big catch.

However, I'm not a naysayer about every stock in this group. I even own some in my personal portfolio and have my eyes on others. Here are my picks for the three best ultra-high-yield dividend stocks to buy right now.

1. Devon Energy

Let me first address one concern about Devon Energy (DVN 0.74%). The energy stock has declined on fears about its dividend. And indeed, Devon did recently lower its dividend payout. But I'm not worried.

For one thing, Devon stock is still up close to 40% year to date even after its decline. Its dividend yield also remains really high at over 9%. The reality is that both Devon's share price and dividend could fall more and the stock would still be one of the biggest winners around.

I think that Devon is in good shape, though. The company offers a fixed dividend plus a variable dividend that's based on excess free cash flow. When oil prices sink (as they've done in recent months), so does Devon's excess free cash flow. However, the U.S. Energy Information Administration doesn't think crude oil prices will fall much more. Neither do I.

Devon's valuation remains attractive with shares trading at only 6.3 times expected earnings. My view is that the tailwinds for the global oil and gas industry will continue to blow strongly enough to make Devon one of the best ultra-high-yield dividend stocks on the market.

2. Enterprise Products Partners

Enterprise Products Partners (EPD 0.99%) is in the energy business, too. Unlike Devon, though, the company's fortunes don't hinge on oil prices. Instead, Enterprise collects the same fees for the use of its pipelines and natural gas processing facilities regardless of how commodity prices fluctuate.

Although Enterprise Products Partners hasn't been what you'd call a high-flying stock this year, it's nonetheless handily beaten the overall market. I expect that 2023 will be another good year for the stock -- especially if a recession is avoided.

Enterprise's yield currently stands at a little under 8%. Is that too good to be true? I don't think so. The midstream energy company is in solid shape financially. It has also increased its distribution for 24 consecutive years. I think that streak will continue.

I doubt that Enterprise Products Partners will beat the market over the next decade based on share price appreciation. However, it wouldn't surprise me at all if the stock did so based on total return.

3. Medical Properties Trust

Medical Properties Trust (MPW) is one ultra-high-yield dividend stock that I don't own right now but have on my radar. The real estate investment trust (REIT) owns hospitals in 10 countries, including the U.S. 

Sure, MPT has been a big loser in 2022 for investors. The stock is down close to 50%. But this huge sell-off makes MPT more attractive, in my opinion, for two key reasons. First, the stock is now dirt cheap. MPT's shares trade at only 6.3 times expected earnings. Second, the REIT's dividend yield now stands above 9.8%. 

I expect the financial outlook for hospital operators to improve going forward. Increased reimbursement rates from Medicare and private payers are on the way. This should make investors more comfortable with MPT's prospects as well.

It's not surprising to me at all that billionaires such as Israel Englander are buying MPT hand over fist. The stock might continue to languish over the near term. However, I like MPT's chances of delivering exceptional total returns over the long term.