A fishy affair

The nobel laurate in physics, extreme weirdo, inventor of the delta function ($$delta$$) and my own personal hero Paul Adrien Maurice Dirac was presented with the following puzzle:

Three fishermen come back from the sea, celebrating the catch of the day.  They land their boat and set up camp. After much drinking (rum?), each collapses in their respective tent. Fisherman #1 wakes up and, after relieving himself, decides to get his share of the catch. He counts the fish, realizes it is not a number divisible by three, throws away one fish to the sea correcting the situation, and takes a third of the remaining fish into his tent. Fisherman #2 wakes up later, goes to pee too, and also decides he is going to get his share of the catch. Unaware that Fisherman #1 already took his part, Fisherman #2 wants a third of the fish he sees. It is not a multiple of three, but he throws away one fish and takes a third of the fish and goes to sleep. Fisherman #3 wakes up after, and does the same: he throws away one fish, takes a third of the fish, and goes into his tent.

What is the smallest number of fish for which this would happen?

I’m not going to spoil the puzzle by revealing the regular answer, but I can tell you Dirac’s answer.  A weird answer, but correct nevertheless.

Dirac prefered to sleep on his left side.

Dirac’s answer was minus two fish.