Savvy investors are always on the lookout for companies that have a long history of paying out high-yield dividends. But that also means being careful not to get caught in the trap in which an inviting yield results from a falling share price and worse, a failing business model.

Perhaps the best example is Pitney Bowes (NYSE:PBI), known for historical dividend increases and dividend-paying stability. If you were to screen the company today for its dividend yield, you’d be pleased to see a 12%-plus number next to its name.

Look a little bit deeper, however, and you’ll find PBI’s dividend may not be stable at all. Indeed, a share price that has tumbled nearly 70% over the past five years is the primary reason the yield is so high. In five more years, PBI may not even be around anymore.

The lesson is clear: Don’t look at dividend yields alone — make sure you understand the company’s fundamentals and business model before you leap. Here are four examples that span the spectrum for high-dividend-yield stocks and whether they get a green, yellow or red light.

Apollo Investment

Dividend Yield: 9%
Red Light

Apollo Investment (NASDAQ:AINV) is a closed-end financial management company that invests in various forms of debt, including senior secured loans, subordinated and mezzanine investments, and equity in private middle-market companies. (Note: Don’t confuse AINV with Leon Black-owned Apollo Management [NYSE:APO]).

AINV’s $2.7 billion portfolio comprises investments in over 50 entities. Revenues are just under $500 million, and its market cap is just under $2 billion. AINV pays out a 20 cents per share dividend, but the share price has languished over the past year, at one point dropping below $7.

And it’s no wonder: Revenues have slipped on a quarter-over-quarter comparison for the last two years, and earnings have followed suit. EPS growth for 2012 is forecast to be down nearly 150%, according to FINVIZ, and is forecast at 5% growth for the next five years. Rather anemic.

Worse news? AINV’s most recent dividend move after the December 2011 payout was to reduce it. I wouldn’t recommend an investment here regardless of the dividend yield.

Southern Copper

Dividend Yield: 9%
Yellow Light

An integrated copper producer that also produces zinc and silver, Southern Copper (NYSE:SCCO) maintains smelting and refining facilities in Peru and Mexico, and conducts exploration in both, in addition to Argentina, Chile and Ecuador.

As the precious metals market goes, so goes Southern Copper, and at least to this point, it’s going quite well. SCCO generates over $6 billion in revenue annually, with over $1 billion of that finding its way to the bottom line. Earnings per share over the next five years are expected to grow nearly 10%, according to FINVIZ. With its net profit margin sneaking up toward the 30% range, Southern proves it knows how to manage costs in a difficult sector.

And nobody will argue with a 92.75 cents per quarter per share dividend, and SCCO has paid a steady, if somewhat fluctuating, dividend since 1996. Looking through charts comparing quarterly net income with quarterly payouts suggests the two are correlated both up and down. So, caution is warrented regarding SCCO’s ability to raise dividends consistently.

Still, if the metals market works in your favor, SCCO could be a very nice play. Of course, I don’t like to play the “if,” so I’d be cautious.

Banco Santander

Dividend Yield: 10.17%
Green Light

If you follow the eurozone crisis at all, you know that Spanish retail banking giant Banco Santander (NYSE:SAN) is deep in the middle of the turmoil. But SAN isn’t strictly a Spanish-centric operation. It operates in the U.K., Portugal, Latin America and the U.S. It has a market cap of over $80 billion, making it one of the world’s biggest banks.

I think this is one of the good guys. It has room to move on both stock appreciation and dividend increases. The shares are up just over 17% in the last year, and the dividend of 20 cents per quarter looks pretty stable.

Fears about both the eurozone and the banking sector appear to be ebbing, at least based on the lack of recent bad news in the former and improved results in the latter. Yahoo (NASDAQ:YHOO) Finance provided forecasts suggesting SAN will improve its EPS by nearly 150% for fiscal 2013, up to 91 cents per share. Five-year revenue growth estimates are for just over 16% per year.

It’s a difficult world for banks, and some pain might still be around the corner, but SAN appears to be one of those high-dividend-yield players that can work long-term for investors.

Six Flags

Dividend Yield: 5.76%
Green Light

Surprised to see an amusement park on this list? Well, Six Flags (NYSE:SIX) makes the grade. It operates 19 parks, with 17 in the U.S., one in Mexico City and one in Montreal.

Six Flags is a great story, having come back from the dead in early 2009 when the stock traded for a mere 6 cents. The company had losses of over $100 million, and it filed for Chapter 11 bankruptcy from which it emerged in 2011.

Six Flags took great pains to increase its attractions and improve the quality of the park experience. Attendance rose, and the company’s recovery doesn’t appear over. As the economy rebounds and people get back to visiting theme parks, Six Flags looks to build on 2011’s $1 billion in revenue.

But the biggest change in the company’s outlook when the dividend, which was at a post-bankruptcy 15 cents per share in February 2011, jumped five-fold to the current 90 cents in just over eight quarters. That’s why this company gets the go-ahead.

As of this writing, Marc Bastow didn’t own any securities mentioned here.