It's no secret that investors love dividends. The quarterly checks provide some instant gratification in the long-term investing game, and reinvesting them can be one of the best ways to make the most out of your money.

But dividend stocks often demand a sacrifice from investors. Companies that make those quarterly payments are generally slow-growers whose days of multibagger investment returns are over. If they believe the best use of their money is simply to return it to investors, they're probably content to grow just a little faster than the economy as a whole. These tend to be businesses with huge brands like Coca-Cola or Procter & Gamble, or industries like energy, telecom, or pharma that generate the cash flow for dividends without a need for massive investment in acquisitions or research and development.

Occasionally, though, an investor can find a high-yielding stock with upside potential in its share price, which usually happens when a dividend payer has been beaten down by the market. This creates not only an opportunity for the share price to soar, but also an ideal investing opportunity, because the dividend yield is unnaturally high. Let's take a look at three such stocks that present these opportunities.

SUPERVALU (NYSE: SVU)
The supermarket parent of Albertson's, Shoppers Food Warehouse, and several other chains, SUPERVALU is one of the biggest value plays in the market. Even after jumping nearly 30% from a pre-earnings-call low last week, the retailer offers plenty of upside potential. Although price-to-sales ratios in the grocery business are generally low, SUPERVALU's 0.04 P/S ratio is about as low as it can go. At that ratio, even a boost in net margin to just 1% would produce a P/E of 4, making shares look cheap.

The company's shares have taken a hit over the last year, due in part to a restructuring plan that meant sizable losses in the last two quarters. With that redirection now in the rearview mirror, SUPERVALU looks like a steal. Analysts estimate earnings of $1.27 for this fiscal year, which gives the company a forward P/E of less than 5. Add a 5.5% dividend yield into the mix, and the reasons to invest look compelling. While the income statement has taken a hit due to the restructuring, SUPERVALU's cash flow remains strong enough to support the dividend payouts.

Niska Gas Storage (NYSE: NKA)
Natural gas has been one of the bigger economic stories over the past year, and dirt-cheap prices due to the supply boom have helped propel stocks like Westport Innovations and Cheniere Energy that stand to benefit from the gas glut. Niska has been on the other side of that bet, however, and its shares have taken a beating over the last year. As United States Natural Gas (NYSE: UNG) -- an ETF tracking natural-gas prices -- has fallen, so has Niska. Gas prices are down more than 60% in the last year, while shares in the storage company have dropped more than 50%.

But Niska is the largest independent natural-gas storer in North America, and it makes money off the volatility in the commodity price -- and by storing gas in the summer, when it's cheaper, and selling in the winter, when prices generally go up. This year's warm winter was among a host of problems that have knocked its share price down, and low prices and stability in gas prices have also hurt its business model. While natural-gas prices have continued to decline, Niska shares appear to have bottomed out, having traded near $9 for the past four months. A change in the direction of natural-gas prices would help the company, as would some volatility in the market. Conditions seem to be at their worst right now, and its business will be in demand due to large supplies. A 15% dividend yield is reason enough to invest, and there are plenty of ways for its shares to turn around and head north. At the very least, the record-breaking warm winter is unlikely to repeat itself.

Telefonica (NYSE: TEF)
Finally, Telefonica presents an appealing opportunity for dividends and stock appreciation. The Spanish company has tumbled in the last year as concerns over that country's economy have grown and Spanish bond rates have risen to 6%. The telecom giant, though, may not be as exposed to the struggling Spanish economy as it appears, since it generates much of its revenue from Latin America. In fact, about 70% of its 2011 operating income came from Latin America and the rest of Europe.

As a telecommunications company, Telefonica provides a needed service with inelastic demand -- unlike, say, Banco Santander (NYSE: STD), another beaten-down, cheap-looking Spanish company that offers a high yield. As a financial institution, Santander figures to have more exposure to the sour Spanish economy and any potential austerity measures imposed. Telefonica's shares, meanwhile have dropped nearly 50% in the last year, and it recently reached a new 52-week low just under $15. As the stock has dropped, its dividend yield has soared, now up to 11.4%. Shares look affordably priced at a forward P/E of just 7, and the company brought in over 8 billion euros in free cash flow last year.

Some more for the road
Beaten-down stocks can be a risky investment, but the reward can more than make up for it. Doing the proper due diligence and research becomes even more important, though, so if you'd rather stick with a safer dividend investment, I recommend taking a look at one of our newest special free reports: "Secure Your Future With 9 Rock-Solid Dividend Stocks." It details a group of dividend stocks, including familiar blue chips and some you may not have heard of, that you can count on to pay you back for decades to come. Click right here to get it.