Replying to T2i video zoom exposure

I have been trying to make video with my 550D/T2i whilst using the zoom and even with everything set to manual and the aperture set so that it doesn't change I get variations in exposure as I zoom. The manual does advise that this may be an issue and I notice on all of the 550D videos I have watched on YouTube that nobody uses zoom - presumably for this reason.

Is there a solution to this - settings/different lens etc?

Any advice would be much appreciated.
Thanks