Diffuser / reflector for garden lantern

I'm making some lanterns for the garden. I want to use maybe three 5mm white LEDs per lantern. The ones I have are narrow beam (+/-10deg) ultrabrights. I'd like to disperse the beam. I have tried the following:

* Abrading/sanding the lens of the LED package
* Mounting in a hole drilled in Perspex
* Pointing the beam at an oblique translucent surface (actually a plastic milk carton)
* Pointing at a ball-bearing
* shining through a plastic 'crystal' bead.

None of these were great although the milk carton seemed best.

Does anyone have a suggestion on how I might get a more diffuse light - or should I source different LEDs?

Thanks