Take them out of the pot and let them cool until you can handle them.

While they cool, prepare a pressure canner: add a few inches of water and the trivet, and bring it to a low simmer.

Bring the syrup, or plain water, to a boil in a separate pot (see notes).

Peel the sweet potatoes. The skins should slip off with your fingers, or use a knife. Cut them into pieces of even size, or leave very small ones whole.

Pack the sweet potatoes into jars, leaving 1 inch headspace, and cover them with the boiling syrup or water, keeping the 1 inch headspace.

Remove air bubbles, adjust the headspace, wipe the rims, and cap with 2 part lids to finger tight.

Load the jars into the canner, lock the lid, and vent steam for 10 minutes before adding the weight.

Process pints for 65 minutes and quarts for 90 minutes at 10 lbs in a weighted gauge canner or 11 lbs in a dial gauge canner, adjusting for altitude (see notes).

Turn off the heat and let the canner return to zero pressure on its own. Wait 5 minutes, take off the lid, and leave the jars in the canner 10 minutes before lifting them out.

Cool the jars on a towel, not touching, for 12 to 24 hours, then check the seals. Refrigerate any jar that didn't seal. Sealed jars keep 12 to 18 months on the pantry shelf.