Look, I don't know whether the market has bottomed out or not after the mess our Congress has made of raising the debt ceiling. However, because my insatiable need for a solid dividend stream is still there, I am always on the lookout for strong earners. Sometimes my dividend-hunting strategy is as simple as running a stock screen with only three criteria: market cap over $2 billion, P/E between 5 and 20, and dividend yield over 8%. Not very sophisticated, I know, but I only use it as a start.

Step two
Using the screen this time, I came up with 16 companies that met my requirements, and from those I culled out just three. How did I make my choices? That's simple, too. I went to my most reliable sources for help, my fellow Fools. By using the Fool.com search function (found conveniently at the top of every page), I checked out each of those companies that looked the most promising.

I read the Foolish articles; I checked out the CAPS commentary; I looked over the stats and statements. And I finally came up with the following three. Don't just take my word for it, check them out for yourself. For your perusal, I present:

A REIT for you
Annaly Capital Management (NYSE: NLY) has been written about frequently here at the Fool, but if we're talking about high, consistent dividends, it's a no-brainer to include it here. Fellow Fool Jim Royal even has it in his World's Best Dividend Portfolio.

Annaly is a REIT, or real estate investment trust, that invests in government-backed mortgage bonds. The lower the interest rates, the bigger the profits for mortgage REITs. Now that even 30-year Treasury bonds have dipped below 4%, Annaly is looking even better.

This company has the highest payout in my small group, with a forward annual dividend yield of 14.9%.  Looking deeper, though, shows us a payout ratio of 107%. For non-REITs, paying out more in dividends than in earnings would be a big downside, but REITs should be treated somewhat differently in this regard.

In particular, when mortgage REITs get income from their investments, they receive not only interest from the mortgage securities they own but also small amounts of returned principal as mortgage borrowers pay off their loans. That extra principal boosts cash flow above interest income, thereby giving mortgage REITs an extra cushion above reported earnings to pay dividends. So as long as payout ratios aren't a lot more than 100%, then the situation is probably sustainable.

Offshore profits
Next in my lineup we have SeaDrill (NYSE: SDRL), an offshore oil well-drilling company I wrote about not too long ago. The oil industry is getting ready for a resurgence of offshore drilling, and SeaDrill is well positioned to take advantage of the increase in deepwater-drilling permits in U.S. waters. The company also has subsidiaries around the globe.

It beats out its rival drilling companies by a large margin with a forward annual dividend yield of close to 8.7%. The payout ratio is a manageable 58%. On the downside, it carries more debt than most drilling companies -- debt that it incurred to increase the size of its fleet. However, it does have the wherewithal to service that debt with an interest coverage ratio of around 5.

Can you hear me now?
Cellcom Israel (NYSE: CEL) is the largest cell-phone provider in Israel. This is definitely not a growth company, as that cell-phone market is saturated, and I don't think the place could handle any more cell towers. It is strictly a dividend play, but it's a good one, with a forward yield of 10.3%. The payout ratio is 69%. Return on invested capital is also quite good. Check this article out for an explanation of ROIC and how it relates to Cellcom Israel.

A concern -- other than the inherent political instability in the area -- is that investors in Israeli equities may be liable for Israeli taxes on any dividends. This is something to check with a tax advisor.

More dividends
These are just a few high-dividend possibilities. Check out our special free report put together by our Motley Fool analysts with 13 more high yielders to choose from.