Adding Name To A List - Alphabetically

I have a spreadsheet with names in column A. These names are sorted alphabetically. I want to add a new name automatically and it shoudl appear at the right position, alphabetically. I wrote the below code, based on the ASCII number of the beginning letter of the name. This does indeed identify approximately where to place the new name. But it's far from easy and I doubt it's efficient.

This is the code I produced thus far....the short version...

Option Explicit

Sub mytest()
Dim firstletter As String
Dim secondletter As String
Dim thirdletter As String
Dim firstletter2 As String
Dim secondletter2 As String
Dim thirdletter2 As String
Dim lowestmatch As Long
Dim secondmatch As Long
Dim firstdifference As Long
Dim seconddifference As Long
Dim thirddifference As Long
Dim myrow As Long
Dim lastrow
Dim cell
Dim empname As String