Your situation
Disagreeing is easy. Making it count takes evidence.
Agencies move against evidence, not against dissatisfaction. The useful step is not a stronger letter, it is a specific criticism of the appraisal, supported by someone qualified to make it.
What to do
The sequence that works
Read the appraisal for the reasoning, not the number
Three sections carry almost all the judgement: the highest and best use conclusion, the after value narrative, and the adjustment grid. The rest is description.
Get an appraisal review
A review appraiser reads the agency report and says whether it is methodologically sound. It costs a fraction of a full appraisal and it answers the question that decides everything else.
Weigh the gap against the cost
If the review finds nothing, the offer is probably defensible and pursuing it will cost more than it returns. If it finds a methodological gap, you have something specific to pursue.
Get an independent appraisal if the gap justifies it
A competing valuation prepared to the same professional standards is what makes a negotiation possible rather than a request for goodwill.
Counter with the evidence
A counteroffer that names the flaw and attaches a valuation is a document the agency can act on. One that says the offer is too low is not.
Honest arithmetic
Sometimes accepting is the right answer
Challenging an offer costs money, and in most states each side bears its own costs, so the fees come out of what you recover. A realistic improvement of a few thousand dollars does not justify an appraisal and a lawyer.
This is why the review step matters. It is the cheapest way to find out which situation you are in, and it is as useful when it tells you the offer is sound as when it tells you it is not.
One question worth asking early: does your state shift fees. A minority of states require the agency to pay the owner’s costs where the final award beats the offer by a margin, and where that applies the economics change completely.
Questions at this stage
How much more could I realistically get
Nobody can say without reading the appraisal and seeing the property. What is generally true is that owners who test the valuation do better than owners who accept without reading it.
Can I do this without a lawyer
For negotiation, often yes. Once a petition has been filed, the deadlines and the procedure make going alone a poor bet.
They said the offer is final
Final offers are frequently followed by further offers, and most cases still settle after a petition is filed.
What if I just refuse everything
The agency files, a court or commission determines compensation, and you are bound by that determination. Refusing without evidence usually produces the agency figure, slowly.
Find the site that answers your question properly
This is a starting point. The detailed answers live on the sites built for each question, and on the site for your state.