1. Paquebot. Mailed on a ship at sea, entered into mainstream at next port. This service allowed whatever stamps were available on the ship to be used as postage (I'm sure someone will correct me on the specifics).
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2. Letter to Chile arrived in Valparaiso uncanceled and the local postal official thought he was doing a good deed by cancelling the unpostmarked stamp.
3. Letter was mailed from Chile with a USA stamp. Arrived in USA as postage due.
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Edit: added example picture(s) from eBay/Hipstamp.