How to implement procedural island generation?

I’ve been wanting to create a procedurally generated island for my game but I can’t figure out how I should do it. The first thing I tried was perlin noise, but it of course created too many islands.

What I want is to create a big island that covers most of the map, and I want it to be centered in the map with an occasional little island next to it. Sort of like this :

![alt text][1]

But I can’t figure out how I would do something like that?

Procedural Landmass Generation by Sebastian Lague