The same way adjusted communicated their offer is a good way to give your counteroffer. I can't tell if their offer is fair without facts. Rule of thumb is damages are 3x medicals for pain and suffering, plus out of pocket losses of wages, property, etc.
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Get a lawyer. The only way you are going to be taken seriously is to hold the threat of a jury trial over their heads. If you are doing this on your own ???? A computer program has pushed out a number at their end. If you only want a little more they may give it to you just to have you go away but you are probably leaving a good deal of money on the table by doing this on your own. Good luck. BTW the last post saying that cases are valued at three times specials hasn't been the case in Massachusetts for quite a while. I don't know what the ins cos are doing in California which is why you need local counsel. But IMHO take the three times specials formula advice with a large grain of salt.
Brother Theodore is 100% correct. Get a lawyer. Statistics have shown that insurance claims settle for an average of 50% higher when an attorney is involved. (I like to think that our firm is above average, and we get results that are above average.)
I feel it is best to give the counter offer in a letter and to give the adjuster a deadline after which time your offer will expire. Also, you should do the math and try to determine if it is indeed worth hiring an attorney. Usually an attorney will enhance the value of the claim, but the difference needs to be substantial enough for you to NET more and it has to be worth the delay in time to get the settlement proceeds. If you have a small case, keep playing the game with the adjuster and do not come down in value too fast. Their first offer is not their last, so negotiate until you are sure that they are done, or hire an attorney to do it for you. Good luck, Claude