Dick W. according to the dictionary on my desk you are correct in your definition of parody. However, the word is very misused nowadays.

To satisfy the pedants among us we probably need some more definitions.

I see several types of songs which for want of a better word are called parodies.

1. True parodies - poke fun at the original
2. ?? - use an original to make a separate humorous comment
3. ?? - add to or amend the original in some way
4. ?? - are another version of an existing song
5. ?? - use an existing tune for a new song

The Shambles,
Sometimes an existing song just seems a better fit than creating something completely new.
This song was written in response to a newspaper story about a woman who had plastic surgery and finished up with a 70 inch bust.
I don't think that it fits the official definition of a parody, as it is not poking fun at the original. I like to think of it as a 'folk' version. Silicone Cindy

Bert.