As the child of a mail carrier, I have to say that I never *saw* him with extra money around the holiday time.
What I did see were tons and tons and tons of cookies and small gifts of food and drink. He does a good job and it was always so cool to see how the people on his route appreciated him.
Letter carriers (if they're doing their job properly; I know a lot don't) do a lot of work for us. Any acknowledgement at the holidays helps lift their spirits out from under the barrage of Special Holiday Catalogues.
