Thanks for the suggestion Giroud.

Ring light? I'm not familiar with that term.

it a way to make sure that light is coming from all around the lens.
you can use a real ring bulb or many small lamp disposed around the lens (or de camera). usually these are soft lamp (like neon tube) that creates no shadow. you should be able to find a ring bulb easily in a supermaket.
in your case (miniumum light required) a ring of small led should be enough too
it is heavily used in music clip (especially R&B) and you can recognize it by the ring reflected in they eyes of the singer.
some use big neon tubes disposed like petals of a daisy flower, the camera being at the center.

Wow ok, i'll give that a shot too. Thanks!