Before the S&P 500 and the Nasdaq Composite Index, there was the Dow Jones Industrial Average. This index includes only 30 companies. But they represent some of the biggest businesses in the U.S.

Most of the Dow Jones stocks offer dividends. An investing strategy called the "Dogs of the Dow" even became popular years ago. The idea was to invest in the 10 highest-yielding stocks in the Dow Jones Industrial Average.

For some investors, 10 is too many stocks to buy at a given time. But three is a reasonable number. Should you buy the three highest-paying dividend stocks in the Dow Jones?

Which stocks make the list?

Let's start by identifying which Dow stocks pay the highest dividend yields right now. Verizon Communications (VZ 1.17%) ranks at the top of the list, with its dividend yield of 7.3%.

The telecommunications giant has increased its dividend for 16 consecutive years. In announcing the latest dividend hike earlier this year, Verizon CEO Hans Vestberg said Verizon is "the strongest cash-generating company in the industry."

Walgreens Boots Alliance (WBA 0.57%) takes the No. 2 spot, with its dividend yield a hair above 6%. Walgreens has increased its dividend for 47 consecutive years and has paid a dividend every quarter for more than 89 years.

The company is best known for its 13,000 or so retail pharmacy stores operated throughout the U.S., Europe, and Latin America. Walgreens also owns an international wholesale pharmaceutical business along with other healthcare businesses in the U.S.

3M (MMM 0.46%) comes in third, with a dividend yield of nearly 5.9%. The company belongs to the elite group of stocks known as Dividend Kings thanks to its impressive track record of 65 consecutive years of dividend increases.

Originally known as Minnesota Mining and Manufacturing, 3M has grown into a global conglomerate. It operates a wide range of businesses in four segments: consumer, healthcare, safety and industrial, and transportation and electronics.

Why are their dividend yields so high?

There are two main common denominators for why all three of these stocks have such high dividend yields. One is positive and the other negative.

On the positive side, Verizon, Walgreens, and 3M have long histories of prioritizing their dividend programs. As mentioned, each company has increased its dividend payout for years.

And on the negative end, these stocks have high dividend yields because their share prices have declined significantly. All three stocks have fallen more than 20% over the last 12 months. Each is also in negative territory so far in 2023, while the major stock market indexes have risen.

Are these stocks good picks to buy?

Growth-oriented investors probably won't like Verizon, Walgreens, and 3M. Income investors, on the other hand, could like two of the three.

I would scratch 3M off the buy list, though. The company has serious litigation risk with lawsuits related to its allegedly defective earplugs and its production of artificial chemicals called per- and polyfluoroalkyl substances (PFAS) that can contaminate food.

Verizon and Walgreens also face challenges. However, my view is that their dividends should be safe. I also think both companies' outlooks could improve. Verizon's balance sheet should become even stronger as its capital investments decline. The long-term demand for wireless should remain strong as well. And Walgreens' earnings have fallen quite a bit. However, Wall Street is generally bullish about the stock, in part because analysts think consumer demand will grow.

Are there stocks you can buy that are even better picks than Verizon and Walgreens? In my opinion, yes. However, for investors looking for juicy dividend yields, both stocks are worth consideration.