Shipping costs and regulations vary wildly from one outfit to anther. I use the post office most of the time so that is the one I am most familiar with:
With USPS there are 3 ways to ship. In descending order of cost they are : Express mail, Priority Mail and Parcel Post.
For priority mail the post office also has a kicker in their pricing called a dimensional (aka balloon) weight. This is a surcharge added for any package over 1 cubic foot but less than 15 pounds and is being shipped more than three zones away. Unfortunately, most dulcimer sized boxes are going to be over 1 cubic foot. They also have a surcharge for "oversized" boxes that are more than 86".....this dimension is determined by the girth of the box plus the length. For example if the box is 10" wide by 10" high by 38" long the size is figured at 78" (40" around the box plus 38"). Increase the height and width to 12" and the length to 40" and the size is now "oversized" (48" around plus 40" long.)
All of this plays havoc with my shipping. As an example I generally use two different sized boxes. One is 10 wide X 10 high X 38 long, the other is 10 wide by 4 high by 38 long. The smaller box is less than 1 cubic foot and is the size I use for student dulcimers because the student model doesn't require as much cushioning or crush space. Well, technically it is supposed to have 2" of crush space all the way around but with the student model I can get away with less. For regular dulcimers I use the larger box.
If I am shipping within a hundred miles or so (staying within 3 zones) the cost for shipping either size box (assuming they are the same weight) is the same. But once I get into the 4th zone things change quickly. The smaller box might go for $12 but the bigger one jumps to $30 plus. And the farther away it goes the bigger the difference. There have been many times when the balloon rate for Priority mail causes the cost to exceed what they charge for Express mail. IOW, sometimes it is cheaper to ship Express Mail than Priority mail. Or it can be cheaper to send two small boxes than one bigger one. A couple of weeks ago I sent 2 student dulcimers to the east coast and it cost about 20 less to ship them in separate boxes. No wonder the post office is going broke....
Then there is Parcel post. Cheap, but it takes forever. I had a dulcimer shipped from Oklahoma City to Warrensburg MO and it took ten days to get here. OTOH I shipped a dulcimer to Arizona last Saturday via priority mail and it was delivered on Monday. IMO, I'd rather spend a few bucks more than have it in the hands of the carrier for 10 days or more.
The post office does have a neat little price calculator at http://postcalc.usps.gov/
which will let you check the various costs.