You can also go to a business like Car Max which will give you a quote for your used vehicle which is good for 7 days. Take the quote with you when going to buy a new car. If the dealer doesn't want to match the Car Max quote as trade-in value, then don't trade in, and sell your car to Car Max.
And/or if you drive cars until they have very little value like I do, just look up the Bluebook value and donate it if you can't get something in the ballpark of your tax deduction from the dealer.
The bottom line is that if you have a figure in mind that's a hard floor, you can just say no; no bargaining required.
Selling it yourself can also get you more money for the old car. If the dealer gets to couple the two deals, they can come down $3000 (say) on the price of the new car, if they can rip you off $3000 on the price they give you for the used one.
