Suggested Rule
This is a rule that is NOT part of the game described by the British Mah-Jong Association.
Rather, it is one of those home grown variations which I am reluctant to lose sight of and which, I think, improves the game, making it easier to collect a more ambitious Mah-Jong hand.
Picking up the discarded tile
The essence of the rule is that the player to the right of the player discarding a tile can pick up that tile, provided it has not been claimed by a pung, kong or Mah-Jong from another player.
The tile so acquired can then be used as if it had been picked up from the wall, except that it cannot be used to convert an exposed pung into an exposed kong.
Consequences
The player who has picked up the tile can use it to form a concealed chow, pung or kong
There will never be a need to claim a chow
(since a chow previously could only be claimed by the player to the right of the discarder)
Picking up a discarded tile may give other players some insight into what is being collected
The player who discards a tile needs to be wary of what he may be offering the player to his right
Collecting a Special Hand, although still difficult, becomes easier
A session tends to take longer to play out
