The stock market's major indices are at or near all-time highs, and as stocks go up, dividend yields go down. As a result, many of the best dividend stocks to buy right now sport relatively modest yields.

That's OK. Because your focus also should be on dividend safety and payout growth that will enhance your yield over time.

Not every stock has been caught up in 2019's surge to new peaks. GameStop (GME), CenturyLink (CTL), Vodafone (VOD), Pitney Bowes (PBI), L Brands (LB), Deutsche Bank (DB) - all of these well-known companies have either cut or outright suspended their dividends this year. Those moves were a blow to all existing shareholders, but especially those who were relying on the income from these sometimes generous dividend payers to tackle regular expenses in retirement.

How do you ensure the dividend stocks you're invested in won't do the same? One way is to monitor the DIVCON system from exchange-traded fund provider Reality Shares. DIVCON's methodology uses a five-tier rating to provide a snapshot of companies' dividend health, where DIVCON 5 indicates the highest probability for a dividend increase, and DIVCON 1 the highest probability for a dividend cut. And within each of these ratings is a composite score determined by cash flow, earnings, stock buybacks and other factors.

These are 13 of the safest dividend stocks to buy right now. Each stock has not only achieved a DIVCON 5 score, but a composite score within the top 15 of all stocks that DIVCON has evaluated. This makes them the crème de la crème of dividend safety - and more likely to keep the dividend increases coming going forward.

Nucor

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Commodity-related companies aren't typically where the mind wanders when it comes to dividend stocks, and especially not as it pertains to consistent dividend payers and hikers. But Nucor (NUE, $55.17) breaks the mold.

Nucor is the leading North American producer of structural steel, No. 2