Pour water to a depth of about 2 inches into a saucepan, place over medium heat, and bring to a simmer.
Combine the lime juice, whole eggs, yolk, sugar, and salt in a stainless steel bowl that will rest securely in the rim of a saucepan over, not touching, the water. (Never let the egg yolks and sugar sit together for more than a moment without stirring; the sugar will cook the yolks and turn them granular.) Place the bowl over the saucepan and continue to whisk until the mixture becomes very thick and registers 180° F on a thermometer. This will take 10 to 12 minutes. If you don't have or trust your thermometer, don't worry. It should thicken to the point that your whisk leaves a trail through the curd.
Remove the bowl from over the water and let cool to 140° F, stirring from time to time to release the heat.
Meanwhile, cut butter into pieces that are 1 tablespoon each. When the lime mixture has cooled a bit, leave it in the bowl if using an immersion blender, or pour it into a countertop blender or food processor. With the blender running, add the butter 1 tablespoon at a time, blending after each addition until incorporated. Taste the curd after you have added 1/2 cup of the butter. If you like the taste, stop adding butter. If you think it needs more, continue adding butter by the tablespoon until it tastes right. (I've been using 1/2 cup butter total.) The curd should be pale yellow, opaque and quite thick.
You can use it immediately, or pour it into a storage container with a tight-fitting lid and refrigerate for up to 5 days. To use after refrigeration, if necessary, gently heat in a stainless steel bowl set over simmering water until it has softened, whisking constantly.