In my experience, you want to add as little milk as possible at first, whisking well, then very gradually add more milk as you whisk vigorously the entire time. From your second line, I think you've got the "small amount" part covered. If you're not already doing this, whisk as you pour - once you start adding milk, I recommend to not stop whisking until the milk is incorporated.
I was also told that you should use warm/hot milk (I give it a quick hit with the microwave) instead of cold. That might be the difference that's causing yours to lump if you're already whisking very well. I don't always heat my milk and still get a good consistency, but I also whisk like a madman. I would recommend trying to the milk and see it if helps.