Depends somewhat on the type of dye (solvent) you use. Slightly dampening the leather seems to help with both spirit and water based dyes. Since the leather is slightly damp, there is less wicking action.
Another alternative is to apply a finish ... Like an acrylic and use a spirit based dye that will penetrate into the finish, but not bleed into the leather. It is a little harder to get a nice even colour, but if you build it up slowly with diluted dye, you can even it out fairly well. If you are going to do it this way, you need to practice on scrap to get the colour and feel that you want.
Tom