There's nothing easy about selecting a dividend stock, especially when the market is trading near all-time highs, as it is now. But if you dig deep enough, you can find some great opportunities that combine high yields and compelling investment opportunities. Three that you should be looking at right now, according to these three Motley Fool contributors, are cellphone giant Verizon (NYSE:VZ), global drugmaker AbbVie (NYSE:ABBV), and utility bellwether Southern Company (NYSE:SO). They aren't exactly set-and-forget investments, but for a little extra work, you'll get a lot of extra yield.

A big payout from a market leader

Brian Stoffel (Verizon): While I don't own shares of Verizon myself, that's largely because I still have over three decades until retirement comes calling. But if my golden years were right around the corner, this company would be at the top of my list.

A piggy bank with the word dividends written above it

Image source: Getty Images.

There are three very simple reasons for this. First, only a few players dominate the telecom space because the costs of building the infrastructure to connect the country are massive. The chance of an upstart disrupting the field -- while possible -- is very slim. By keeping an eye on AT&T and T-Mobile, you can have a pretty good idea where Verizon stands.

Which brings me to my second point: Verizon is the leader in its industry. It has the highest market share of mobile plans in America, and it was the first to market with 5G technology. As a result, it will likely be able to charge more for its plans, and open the door to more Internet of Things (IoT) revenue.

And third, the dividend is big and sustainable. Currently yielding 4.2%, Verizon's dividend has only eaten up 54% of the company's free cash flow over the past year. That means the payout is very safe, and there's even room for it to go up in the long run. 

A falling knife worth catching

George Budwell (AbbVie): AbbVie, a dividend aristocrat, has suddenly turned into a falling knife. The loss of exclusivity for its flagship anti-inflammatory medication Humira in Europe, a major setback in immuno-oncology with Rova-T, and the steady decline in its hepatitis C franchise have all conspired to drive the drugmaker's shares down by a whopping 30% over the last 12 months. However, this steep sell-off might represent an extremely attractive entry point for income and value investors alike.

After this sharp downturn, AbbVie's shares now sport a ginormous 5.4% yield and are trading at a rock-bottom 8.4 times forward-looking earnings. That's a rare combination for a top pharma stock, implying that the market has been far too harsh on the company. The market, in effect, is saying that it won't be able to overcome Humira's eventual demise as the world's top-selling drug. This dire outlook, though, flies in the face of the facts.

Why should investors give AbbVie a second chance? The biotech's hematologic oncology portfolio -- consisting of Imbruvica and Venclexta --has been performing beyond expectations this year. And the recent approval of Skyrizi for moderate to severe plaque psoriasis gives AbbVie yet another major growth driver to power past Humira's patent cliff. The company could also receive another big boost from the approval of upadacitinib for rheumatoid arthritis in the third quarter of this year.

AbbVie has built a healthy portfolio of new products capable of keeping its growth engine humming along at full speed. The market will want solid proof of this thesis once Humira goes off patent globally, but the risk of a moderate drop-off in sales early in the next decade seems to be priced in at these bargain-basement levels.    

A clearer path to completion

Reuben Gregg Brewer (Southern Company): At 4.6%, Southern's dividend yield sits at the high end of the utility spectrum. The reason is that it has been having some troubles getting big projects over the finish line. First, it had to give up on carbon capture technology it helped create for a coal plant (it eventually converted the plant to natural gas). And, perhaps more troubling, it has been forced to take operational control of a nuclear project that has faced delays, cost overruns, and the bankruptcy of Westinghouse, the original contractor.

SO Dividend Yield (TTM) Chart

SO Dividend Yield (TTM) data by YCharts.

To make matters worse, Southern still has a couple of years of heavy lifting (and spending) before its nuclear ambitions are realized. The planned start dates for the two nuclear units it's building are November 2021 and November 2022. However, it just completed a review of these projects, known as Vogtle 3 and 4, and it looks like it has built up a six-month cushion to deal with any problems that might arise. If there are no more troubles, then the units could actually come on line early. 

As investors get more comfortable with the improving results at the Vogtle builds, they are likely to feel more comfortable with Southern's stock. (Southern is much more than just the Vogtle project.) And that, in turn, could lead to higher prices and a lower yield. Although there's still a lot of work to be done, all indications are that Southern has gotten this project back on track. That makes now a good time to jump on the fat yield it's offering today.