This is one of the reasons that you'll often see sweepstakes void in certain states. This is also the main reason that you find a lot of smaller prizes available in sweepstakes. If this is your first time sponsoring a sweepstakes, make sure you check with local laws about possible restrictions. Local marketing and promotion agencies can help you with this information. The way you handle your promotion will show people whether or not your promotion is legitimate.
Legitimacy is the key.
Many sites hold a sweepstakes just for the sole purpose of gathering names. For example, one site chose to give away a custom designed T-shirt every month as the grand prize. Create a nice graphic, or coupon, or order form with the discount posted right on it. Don't hide it or disguise it as a sweepstakes. If you hold a sweepstakes just for the sole purpose of gathering names, you are quickly going make a lot of enemies on the Web.