You have a bit of leverage because of the "injury". They don't know if the injury is going to come back and bite them in the ass...........who knows if you've got ongoing back problems yet. If you settle for a fixed amount, you waive all rights to any claim to them for any future problems relating to this incident. They'd rather pay a bit more right now and be out from under any possible medical issue down the road.

Personally, with no ongoing injury, an offer of $4K is eminently fair. It's unlikely that an attorney can get any more money unless he does some creative work with regard to the "injuries". You're entitled to be made whole.........you're not entitled to take more from the insurance company than you need to be made whole.

The few additional dollars above your actual losses can be considered as payment for you accepting any future risk of ongoing injuries from the accident.