how do I get rid of adapters / linkers after ligation to my cDNA

[Ralf Sigmund]

Hi,
I am trying to digest ds-cDNA with a four base cutter Restriction Enzyme.
Afterwards I ligate an adapter to both cutted ends.

I now want to PCR-Amplify my cDNA Fragment with Primers in the Adapter
regions.

This apperently fail because the PCR is completely dominated by
Adapter-DImers.

So I would like to get rid of theese 58 BP Adapter dimers.
However the amount of cDNA is very limited, so I fear to loose too much if I
run an agarose Gel...

Thanx for any hints
ralf