I have the following timeline:

<clip1-8secs><clip2-3secs><clip3-3secs><clip4-3secs><clip5-20secs>

I wish to have a short fade between clip2 and clip3 but when I try to use the Cross Dissolve transition in Adobe Premiere Pro CS3, I get a message stating "Insufficient media. This transition will contain repeated frames."

Any idea how I can solve this?

For starters your clips are very short and then there is that problem only Premiere seems to have and that is concerning 'handles'. If you can capture your clips again and in the capture screen down in the bottom right you will see 'handles' highlighted in blue with the number 0 beside it, try changing this to a higher number and see does this improve things.

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Better than a poke in the eye with a pointy stick any day...

even though you get the mesage have you still gone ahead with it...I did a quick test...and as far as I can see....the crossfade still works.....you can alter the length and/or star position of the crossfades....sometiimes with short clips like that I like to turn off "snap"...drag them slightly apart and add cross disolve to the end of one and the start of the other....then alter the length of disolves...looks quite effective and arty almost going to black quickly

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www.whinbushmultimedia.co.uk named after the Whin bush, (Gorse) that grows where we live in Northern Ireland.

If you would hilight the transition by clicking on it and then open the "Effect control" panel you will see how much you need to trim the video in order to get proper length. the deal is simple, if you applying transition one second you will need one second of video clips and since you placing it in between clips you will have to trim 15 (or 12 depends on the frame rate of video) frames of from each clip and so on.
The reason premiere give that message is that simple. It will repeat the frames in order to cover the length of the transition.