[elcid1970]

IIRC this was last done to pass the 21st Amendment repealing Prohibition. A Constitutional convention bypasses a lot of local politics & it did so in this case (notice the 21st repealed the 18th but left up to the states the re-legalization of alcohol).

[Publius]

First off, the 21st Amendment was proposed by the usual mechanism. Two-thirds of the House and Senate passed it and sent it on to the states for ratification. There was not an Amendments Convention on the topic.

However, Congress, as part of its Disposal power, sent it to state ratifying conventions, not state legislatures, for ratification. Each state held a special election to fill a state ratifying convention based on the makeup of its most numerous, i.e. lower, house.

A state ratifying convention is different from an Amendments Convention involving all the states.