Under 13 ounces, I use a padded envelope and ship First Class. I use a scale. It costs more for me to ship over 13 ounces from Maine to California than it does for instance, from Maine to New York. So Cali might get flat rate while NY gets a weighed box or envelope. By using a scale or Flat Rate boxes and Click'n'Ship at www.usps.com, I pay less than the Post Office price on all Priority Mail. USPS will even send you free shipping boxes and envelopes so you will use their service. My favorite is the Legal Size Flat Rate Envelope. I think the price may have just gone up, but it was $5.55 if one prints the label at home. You don't need a scale for that one. Just stuff as much as you can fit. They are flimsy, so I go around the edges with packing tape and use an inner cover of cloth, news paper or Tyvek. Small boxes fit inside the inexpensive envelopes too.
I am a bike mom....I have shipped a gazillion bike parts on eBay for my son. Rhizomes are easier. If they get broken, just plant the pieces.
So, for a few rhizomes, First Class works.
