I'm surprised that no one's mentioned "Come all you fair and tender ladies," which as I recall it contains the "killing crime" verse cited by Rob and has a very different tune from any of the "Love is pleasing and love is teasing" songs. For that matter, I'm not convinced that they're all the "same song" -- I know that RISE UP SINGING mushes them all together under "The Water is Wide" but I associate different melodies for the different "variants," including the single-verse variant sung by Lizzie Higgins (Jeanie Robertson's daughter):
   "Love it is teasing, and love is enticing;
    O, love come beside me and keep me warm;
    But when it grows older, love it grows colder,
    And it just fades away like the dew on the rose."
It's frustrating that she only sang the one verse to a melody that I wish I could reproduce here; it's eerily different, and if anyone know any other verses she sang (or could have sung) to it, I'd love to hear them.