Have you been offered a free flight or “cash back” for opening up a credit card account? If you’ve got excellent credit and took the bait, you may have left something on the table.

If you pay your credit card in full every month, you deserve big rewards for your loyalty. The struggling economy has forced banks to increase their sign-up bonuses to compete for a shrinking pool of customers with excellent credit. So savvy reward-card users with good (and sometimes even just decent) credit scores shouldn’t even consider applying for a card unless it offers sign-up bonuses worth more than $750.

And that should matter much more than the actual rewards the card offers.

Sound weird? Think of it this way…

Picture a successful professional earning $90,000 who charges $30,000 each year on her credit card. Even a rewards credit card offering 2 percent cash back (which is double most cards) will return just $600 in rewards. That’s less than many sign-up bonuses these days.

I regularly sign up for new cards and drop my old ones just so I can score these hefty deals. I don’t keep too many cards open at once, because that can affect my credit score. Oddly enough, repeatedly signing up and dropping credit cards doesn’t have a big impact on my credit score – certainly not enough to deter me from all the money I’m saving.

So far this year, I’ve signed up for two credit cards – and earned an $1,100 statement credit from Capital One’s Match My Miles promotion and 100,000 miles from the British Airways card. Those miles are enough for a round-trip ticket to Europe in business class, worth several thousand dollars.

While those offers have since expired, there are still some great sign-up bonuses out there…

1. Southwest Airlines Rapid Rewards Premier Card

Sign-up bonus: 50,000 points with your first purchases – enough to pay for $830 worth of tickets. Since less expensive flights consume fewer points, this is ideal for those taking many short flights. Warning: There’s a $99 annual fee, and it’s not waived the first year like some other cards.

Rewards: Most purchases only earn 1.6 cents per dollar spent, so you’d have to spend $50,000 to earn as much as you did from the first dollar you charged.

2. Chase Sapphire Preferred

Sign-up bonus: 50,350 points, but they’re only worth $625 toward travel purchased at Chase’s Ultimate Rewards website. Fortunately, you can use the credit toward any travel purchase, not just flights from a specific airline. The $95 annual fee is waived the first year.

Rewards: Like the Southwest card, you’d need to spend $50,000 on most purchases to equal the same points you got from the sign-up bonus. But Chase has just improved this card by offering double points for travel and restaurant spending and triple points for travel purchases made through their website.

3. US Airways Premier World MasterCard

Sign-up bonus: 40,000 miles in US Airways’ program to cardholders who spend $750 within the first three months. Normally, this would leave you just short of two free flights. Thankfully, US Airways offers cardholders a 5,000-mile discount when they book an award flight, so the bonus is worth two domestic economy seats. The $89 annual fee isn’t waived.

Rewards: This is a standard airline card, so you only get one mile per dollar for most purchases. But you do get perks such as access to first-class check-in lines, priority boarding, and a pair of $99 companion tickets.

4. Starwood Preferred Guest American Express Card

Sign-up bonus: 30,000 points. This doesn’t seem like much, but these “Starpoints” are extremely valuable toward luxury hotel stays, as well as transfers to miles with 30 different airline programs. Transferring 20,000 points to miles earns a 5,000-point bonus – so at this rate, the bonus is equal to 37,500 miles, with your choice of dozens of different frequent-flyer accounts.

Rewards: There’s easy availability of free-night awards, flexible point transfers, and great customer service, which makes the Starwood card a longtime favorite among reward-travel experts.

5. British Airways Visa Signature Card From Chase

Sign-up bonus: Yes, you missed the incredible 100,000-mile promotion, but the regular offer is still 50,000 miles for spending $2,500 in the first 90 days. To make the most of this bonus, spend another $30,000 in a calendar year to receive a free companion award certificate, which doubles the value of your miles.

Rewards: You still earn 1.25 miles per dollar spent with this card – better than most airline cards. British Airways miles can also be used for flights on American Airlines, which has generous award seat availability.

Conclusion: If you have decent credit, don’t be lured by attractive rewards offers if they don’t also come with big sign-up bonuses.