The term used is apparently ***air courier***. I've found several resources on the topic after more searching.

But I have not found the names of any courier companies. They seem rather elusive!

**TL;DR version:**

- It *does* still exist.
- It *has* become a lot less prevalent, but only partly due to post-911 security changes.
- The savings are far smaller than they used to be.
- They use your checked luggage, not your hand luggage.

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**Sources:**

- WikiVoyage actually has [an article on air couriering][1].
- `about.com` has [a good article][2] too.
- There's [a writeup here][3] on a website called `seminar.org`.
- A company called ["Air Courier International"][4] has information specifically detailed for the [UK][5] and [USA][6].


  [1]: https://en.wikivoyage.org/wiki/Air_courier
  [2]: http://budgettravel.about.com/cs/aircouriers/a/mission_courier.htm
  [3]: http://www.seminar.org/courier1.htm
  [4]: http://www.aircourierinternational.com/
  [5]: http://www.aircourierinternational.com/uk-courier-flights.php
  [6]: http://www.aircourierinternational.com/us-courier-flights.php