Blindly buying dividend stocks with sky-high yields can be a recipe for disaster. A high dividend yield often comes with an elevated risk that the dividend isn't sustainable.

AT&T (T 1.02%) and British American Tobacco (BTI -0.51%) are two stocks with exceptionally high dividend yields, but in each case, the dividend looks safe. Both companies are facing challenges, but that shouldn't deter dividend investors from scooping up shares of these high-yield stocks.

AT&T

Telecom giant AT&T is doing just fine. The company continues to win wireless subscribers, despite a post-pandemic slowdown, and its fiber internet business is growing rapidly. AT&T has stuck with its guidance calling for at least $16 billion of free cash flow in 2023 and plans to make significant progress paying down its debt over the next two years.

The company's dividend is well covered by the company's free cash flow. While the dividend was slashed as part of the spinoff of WarnerMedia, the current dividend looks sustainable.

Investors receive $0.2775 per share each quarter from AT&T, which works out to a dividend yield of about 7.9%. The dividend will eat up about $8 billion of cash over the next year, based on the current share count, or roughly half the company's free cash flow.

AT&T will prioritize paying down debt over any dividend increases, which is the right move. As the company refinances debt as it matures, new debt will likely carry higher interest rates. That will put some pressure on free cash flow as interest payments rise, but reducing the debt load can counteract higher interest rates, to a degree.

Barring a catastrophe, AT&T's dividend looks safe. On top of a high-yield dividend, the stock's valuation is so beaten down that the potential upside for investors is enormous, even if AT&T's financial results don't materially improve. All it would take is a sentiment shift leading to a less pessimistic valuation.

AT&T stock trades at a price-to-free-cash-flow ratio of roughly 6.3. The stock certainly doesn't deserve a premium valuation, given its sluggish growth prospects and debt-heavy balance sheet. But this seems overly pessimistic.

While AT&T could run into problems winning wireless subscribers if the economy worsens, the stock price has a big margin of safety built in. With a dirt cheap valuation and a high-yield dividend that appears sustainable, AT&T stock looks likely to deliver for investors in the long run.

British American Tobacco

Cigarette consumption, particularly in the United States, is in a long-term downward trend. British American Tobacco is doing two things to grow revenue in this environment. First, it's pushing up prices. Overall combustible revenue rose 0.2% globally in the first half of 2023, with volume declines offset by a 6% bump from pricing and mix.

Second, British American Tobacco is rapidly growing its non-combustibles businesses, which include vaping. Revenue from what the company calls "new categories" has grown by 33% annually since 2019, and British American Tobacco is on track to reach 5 billion pounds by 2025. These businesses are almost profitable today, and the company expects them to reach profitability in 2024.

Overall, British American Tobacco delivered revenue growth of 4.4% and adjusted earnings-per-share growth of 5.3% in the first half of 2023. These results should give investors some confidence that the company can not only sustain its dividend, but also grow it over time.

While currency-exchange rates affect how much holders of British American Tobacco's American Depository Shares receive each quarter, the stock currently sports a dividend yield of about 8.6%. The company aims to maintain a dividend payout ratio of 65% in the long run, so the dividend can grow right along with earnings.

Slow growth is the most you can expect from British American Tobacco, but with a sky-high dividend yield, that's more than enough to produce solid results for investors.