Step 1 Combine the salt and sugar. Lay the salmon in a flat shallow container skin-side down and rub with the salt-sugar mixture. Cover with plastic wrap and refrigerate 24 hours.
Step 2 Bring the salted water to a boil; stir to make sure the salt is dissolved. Cool. Pour over the salmon (the liquid should cover the fish), cover and refrigerate for 24 hours.
Step 3Remove the salmon from the liquid and pat dry. Use a very thin, sharp knife to slice the salmon thinly on the diagonal. Serve with lemon wedges.