The Priority Mail Large Video Box (O-1096L) may be the U.S. Postal Service's best kept secret. It's not a very big box (9.25" x 6.25" x 2"), but it holds quite a bit more than the Small Flat-Rate Box, and if you're shipping internationally—or at least to Switzerland; I haven't had need to try any other countries recently—it's the same price.
You can get the boxes for free from the USPS, too. The trick is knowing what to order. The box is O-1096L, called "Priority Mail Large Video Box." You see, it's not flat rate domesticaly, only internationally. But the kind USPS lady on the phone—whom I called in desperation, being unable to find a "flat rate" version among their shipping supplies— assured me that this is the right box to use, though she admitted that some local post offices haven't gotten the word yet that it's flat rate for international shipments. I've used it successfully twice so far.
It's a real bargain over the regular Priority Mail or First Class International prices. If you print the postage online, the cost is even less, and you can fill out and print the Customs forms at the same time. (The form from the post office is a bit simpler, however.)
UPDATE: Apparently most post offices don't carry these boxes. You can get them free from USPS online, but it does take time.
UPDATE 2: I forgot to mention that in order to get the $13.25 price you must pay for the postage online and print it yourself; if you pay at the post office, the price is $13.95. We've found it well worthwhile to set up the ability to pay online, as the price is almost always better.
UPDATE 3: Did I mention that this is the Postal Services best-kept secret? Unfortunately, they're also keeping it from many of their employees. One person I know went to two different post offices, only to be told each time that the postage cost for her package would be over $30, because the box doesn't say "Flat Rate." What's more, they refused to call, or look it up online, although one branch said they'd look at a printout if she brought one.
Later, when she herself called the main USPS customer service, the representative confirmed the flat rate (after sighing, "Oh, the Video Box problem again"), but added, "Good luck convincing a local post office if they don't believe it. It's at their discretion whether to accept it or not."
WHAT??? The local post office can decide, willy-nilly, what to charge for the U.S. mail? This is carrying privatization a bit too far, don't you think? Actually, I don't believe it. She's going to try a third, larger, post office (after calling ahead, and bringing printouts with her just in case).
I think the wonderful folks at our own local post office deserve a large plate of Christmas cookies this year: they're always friendly, always helpful, and they've never given me any trouble.with the Large Video International Flat Rate Box!
UPDATE 4: I half take back my harsh words in Update 3. The post office that said they'd consider changing their minds if they saw proof apparently decided to look it up themselves, and today gave almost no trouble: The first clerk refused, but the one next to him overheard and said, "No, no, it's okay, she's right. We looked it up." It would have been nicer if they'd been willing to look it up the first time, but at least they're all educated now.
UPDATE 5: As you can see by the comments below, people are still having trouble with this, depending which post office they use. As I said, "Educating the world, one post office at a time." The bad news is that, since the recent postal rate increase, the cost of the flat-rate box has risen considerably. It is now $16.95, with no discount for paying online. :( But it's still better than First Class (currently the least expensive international option (at least to Switzerland, and I'm assuming to most countries) if your package weighs more than 1 pound 12 ounces.
UPDATE 6: (12/14/13) Well, it once was a great deal. Now it's $23.95. Unfortunately, I still have to call that a reasonably good deal—compared with other overseas rates. The demise of international book rate, and then international parcel post ("boat rate") has been a sore trial for those with family overseas.
UPDATE 7: (3/14/16) I don't mind occasionally paying more in postage than the value of the item sent. Otherwise I'd never send homemade cookies, or Hallowe'en candy surprises. But the cost of this box, which is still in most cases the least expensive option, is has now risen to $33.95!