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'Inspect' the trade while the customer is watching. Use clipboard. Make up a form if you have to. Remain silent as you touch every crappy looking part of their car. It's ok to do a few 'hmmms'. The customer knows there is stuff wrong with the car and they now know you know.
Whatever the appraisal comes back as, knock off a thousand or two. Give the customer a chance to agree. You have nothing to lose and a pound or tow of commission to gain. Do it. Don't be a weak suck girl about it. Ok?