I got the correct rules fro this site - http://people.ucsc.edu/~rosewood/cards.html
Thirteen card tracheotomy
The object of the game is to discard all your cards.
Each player is dealt thirteen cards.
The player with the lowest card (see "ranking cards") begins play and discards an allowable hand. (see "allowable hands").
Play continues clockwise, each player either passing or discarding an allowable hand. In each round, players must discard the same number of cards as the preceeding hand. For example, if the first discarded hand was a pair, only pairs are allowable discards, and no more. If the first discarded hand is a single, only singles are allowable hands for discard.
You may pass at any time, you are not forced to discard if you can.
Play continues until all players have passed. The last person to discard may now discard any allowable hand. That is, it is at this point that the restriction against changing the number of cards in the allowable hand is lifted. This is a key part of the strategy, and a player who was the last to discard, and all other players having passed, is said to be "In Control." Play continues until one player discards all cards.
If a player has only one card left, the player must announce "last card." No announcement is required if the last cards are a pair or other multi-card hand.
Ranking cards
Suits are ranked from lowest to highest thus: diamonds, clubs, hearts, spades
Pips are ranked from three lowest to 2 highest.
Therefore the two of spades is the highest card; the three of diamonds is the lowest. When determining who begins the game, in a four-handed game, the person with the three of diamonds begins. With three players, if no one holds the 3 of diamonds, then the player with the three of clubs, or hearts, or then spades would go first.
Allowable Hands
The following hands may be discarded. The five-card discards are listed in rank order.
one card
a pair
three of a kind
five card hands
full house
straight
flush
four of a kind and any other card
straight flush