The major credit card companies all covet the same customer segment these days — big spenders who pay off their entire bill each month, but still generate healthy profits because they swipe their plastic so often.

To woo these more affluent shoppers, American Express (AXP), Bank of America (BAC), Citigroup (NYSE: C), Capital One Financial (COF), Discover Financial (DFS) and JPMorgan Chase (JPM) are locked in an intense competition over card rewards.

The card companies are trying to strike a tricky balance: holding the line on their rewards payouts to customers while simultaneously stealing market share from their foes. The result has been a slew of offers designed to poach other firms' customers, often through the promise of introductory rewards points, and then to make them loyal to their new brand.

Though industry-wide data is scarce, it appears that rewards offers are becoming more generous. Capital One, for example, recently rolled out a rewards card that offers 1.5% cash back on all purchases at all times. Other cards might offer more cash back, but only on specific purchases.

"We are definitely seeing the average rewards value increase over time," says John Kiernan, senior analyst at CardHub.com. "And obviously the people who really win out in this are the really savvy consumers."

At Discover, the highest base rate for cash rewards was 0.5% in 2010 and 1.0% in 2013, according to data compiled by Bankrate.com. In its most recent annual report, the Riverwoods, Ill., company stated that competition based on cash rewards had increased in the two previous years.

Bank of America and Capital One also increased their highest base cash rewards rates between 2010 and 2013, according to Bankrate's surveys, while American Express, Chase and Citi held the line.

There are several reasons why card companies are vying so hard for affluent customers who pay their entire bills each month.

These customers tend to have low default rates, and because they're not carrying a balance, issuers don't need to hold as much capital against their accounts. Furthermore, regulatory changes in the last few years have made the lower end of credit card business less lucrative.

Analysts expect the fierce competition for big spenders who pay reliably to continue. "The way you get those customers is through rewards," says Scott Valentin, an analyst at FBR Capital Markets.

The arms race among issuers is most intense with respect to introductory rewards offers, which are designed to encourage customers to switch.

Capital One's VentureOne Rewards card provides one example of the sweet incentives consumers are being offered today. The card gives new customers miles redeemable for $50 in cash, or twice that amount in travel, as long as they spend $1,000 during the first three months they have the card.

A new survey by Bankrate finds that such introductory bonus offers are becoming more common. "They're far more prevalent now," says Greg McBride, senior financial analyst at Bankrate.

Once a high-spending consumer switches cards, issuers are going to great lengths to hold onto them. These efforts take a variety of forms, including making it easier to use points for different types of purchases, and simplifying the process of redeeming points.

"It used to be it was a little harder to redeem your rewards," says Valentin. "The redemption options have gotten a lot better."

Companies also are trying to increase customer engagement with their cards by offering rotating bonus reward categories. Hence the ubiquitous offers for 2% to 5% rewards at gas stations, or supermarkets, or restaurants, but often only if the customer takes a proactive step to activate the deal.

In a recent call with analysts, Discover Chief Executive Officer David Nelms argued that the firm's rotating 5% rewards program has drawn customers closer to the company.

"A lot of it is not about the rate," Nelms said. "It's also: how easy is it to redeem, how can you redeem with various partners? What categories is it in, during what [time] of the year? We've got customer service people that actually work with our customers to help them maximize the benefit."

The potential downside of Discover's strategy is that it gets complicated for the cardholder. Especially for consumers with more than one credit card, it can be hard to keep straight which piece of plastic offers the best deal at a particular time and place.

Capital One is trying to capitalize on customer confusion with Quicksilver, a new card that offers 1.5% cash back on all purchases. "We specifically designed this product for cash back rewards seekers that want to effortlessly maximize their returns," a Capital One spokesperson wrote in an email.

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Corrected July 1, 2013 at 3:15PM: An earlier version of this article incorrectly stated that Capital One's VentureOne Rewards card gives new customers miles redeemable for $500 in cash, or twice that amount in travel, as long as they spend $1,000 during the first three months they have the card. The cash amount redeemable is $50.