I have a completely different, but very simple method of making a basic white sauce (probably not strictly a Béchamel, as it's a different recipe) that doesn't involve making a roux. It also doesn't use butter, making it lower fat. I use semi-skimmed milk (2% in the US), and it works fine every time. I use it in lasagne, macaroni cheese (mac & cheese in the US) etc.
I put a heaped wooden spoonful of cornflour (cornstarch in the US) in a saucepan, then add a slug of milk - enough to fill the pan about 3mm (1/8th of a inch) deep. Then I stir it for 20 seconds or so, pressing the lumps out with the wooden spoon to get a smooth thickish paste, then stir in the rest of the milk (probably about 20 fl oz, 550ml, I never measure it) and heat it, stirring a lot. If it starts to thicken too much, I add a bit more milk and whisk it in. Just keep stirring till it's thick, smooth and glossy. Season a little and it's done!
It really is that simple, and you don't even need to heat it until all the milk is in.