If you don't like the automatic template provided by Picnik, you can create custom postcards online using your own design created right in the basic editor on the site. You won't have the features for adding a message or automatically sending it to recipients, but you do have more flexibility with your design.
This example utilizes the vignette effect and the rounded corners frame. Two text boxes were added and could be placed anywhere on the photo, unlike with the postcard template.

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When it comes time to print custom postcards, you'll want some heavier paper that will be able to handle going through the mail. You can buy your own or go to a digital photo printing kiosk nearby. Make sure you print in the right dimensions (4x6 or 5x7) so that you'll only need one stamp to send out the postcard. Once you're done, just add your message, address and stamp and you're good to go!
You can also save the custom postcards as a JPEG and send them out to friends and family via email, or post them on your blog, Facebook page or other social networking site to let everyone see where your travels have taken you. Check out Picnik's website to see which option works best for you.
You may also be interested in reading Upgrading to Picnik Premium: What are the Benefits?