All 30 Dow Jones (^DJI -0.11%) components pay a dividend these days. But they're not all the same. Dividend yields range from 0.8% to 5.2%. Some companies are committed to growing their dividend checks every year and some are not. And there's a wide variety of headroom for further dividend growth. With all these variables on the table, it ain't easy to pick a great dividend stock among these 30 blue-chip champions.

I'd like to poke at Dow member American Express (AXP 0.07%) today. The credit card issuer currently offers the second-lowest yield on the Dow,  just 1.1%. And the company hasn't exactly put its back into dividend boosts lately, growing payouts by a modest average of 3.6% in the last five years.

Is there any hope for this thoroughly unexciting dividend to ever become a serious income-generating investment?

On the upside, American Express moves just 19.6% of earnings into dividend payouts. That leaves a ton of headroom to increase the dividends further and faster. But don't get too excited over this faint glimmer of hope, because...

AXP Dividend Yield (TTM) Chart

AXP Dividend Yield (TTM) data by YCharts.

To put it bluntly, American Express has never showed any interest in producing a great dividend. If not for the drastic share-price drop during the 2008 financial crisis, American Express would probably never have offered a yield north of 2%.

The long, slow drop toward the 1% yield line looks mighty comfortable in a historic perspective. It's how American Express rolls; don't expect a sudden change of heart as long as the present board of directors stays more or less intact.

And it doesn't help much to look across the credit card sector for a white knight. None of the major credit card companies like to put much strain on their dividend payout ratios:

AXP Payout Ratio (TTM) Chart

AXP Payout Ratio (TTM) data by YCharts.

Visa (V 0.33%) offers an even thinner dividend yield (0.8%, making it the lowest Dow yielder), and non-Dow company MasterCard (MA -0.07%) makes them both look generous with a forgettable 0.3% yield.

Don't hold your breath  waiting for American Express to become a great dividend play. The massive cash machines in the credit card industry are simply not set up to reward shareholders this way.

It's a different story if you're looking for fantastic growth stocks, as all three of these tickers have crushed the Dow in 2013. But that's a whole 'nother ballgame.

AXP Chart

AXP data by YCharts.