[Code] subset duplication

One of the step in test driven development is "refactoring your code".
One of the main step of refactoring is the act of removing duplication.
You can read from wikipedia: "The concept of removing duplication is an important aspect of any software design".
I think duplication is pretty difficult to identify; there are a LOT of different kind of duplications. Some of them are stated here.
Today i notice another kind of duplication, something i can call like 'subset duplication' where a function does a little less of another bigger function.

For example:
addTicket(id, value) and
addTicket(id, value, comment) and
addTicket(id, value, date)

I think it's better to have only one function without say the same thing in one thousand of little different modalities. I like expose the differences, not hide them.
One solution could be addDefaultTicket() that return a ticket so you can customize with fluent interfaces: addDefaultTicket().withComment("xxx").
I think there are plenty of other solutions, but the point is always the same: trying to find the best and unique solution.