Pick over the crabmeat and discard any bits of shell.
Mix the mayonnaise with the ketchup, Tabasco, mustard, lemon juice, and tarragon.
Stir in the crab and spring onions. Taste and play around with the balance of flavourings until you get a perfect balance (but hold back - too much tasting will leave your guests with woefully diminished portions!).
This can be mixed together an hour or two before serving, but bring back to room temperature before assembling the finished cocktail and serving.
Remove the outer leaves of the Little Gem lettuces and shred the rest thinly. Place in a plastic bag and leave in the fridge until almost ready to serve.
Take 4-6 sundae glasses or old-fashioned champagne glasses. Divide the lettuce between the glasses and top with the crab cocktail. Serve straight away.