Every situation is different and yours may depend on what the doctor is willing to settle for and whether you will make payments or a lump payment.
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Debt collectors can be aggressive without breaking the law but certain practices are illegal. If you think that the collection company has crossed the line contact an attorney, like me, that is familiar with the Fair Debt Collection Practices Act. As for settlement, it is hard to predict what might happen. You will likely get a better discount if you can pay a lump sum. Many debt collectors will insist on complete (or nearly complete) payment if a payment plan is agreed to. Make sure if you negotiate a payment plan that you can honor your commitments because some collection companies will include provisions in settlements that allow them to accelerate collection if you miss a payment.
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Any settlement depends upon two factors: (1) the amount that you are willing (and can afford) to pay and (2) whether your doctor is willing to settle and for how much. In my own practice, I've had a fair amount of success in offering a smaller, lump sum payment in lieu of the full amount paid over installments. That said, it's best to consult an attorney in order to determine whether this path best suits your needs.
Like the previous attorneys have said, a lump sum is the best way to handle it. How much you should offer depends on several factors, the most important being how old the judgment is. The closer it is to 6 years old, the larger the discount you can ask for.
One strategy I have used in the past for smaller amounts may yet work for you. Contact the doctor directly, give him your sob story, apologize for your tardiness, ask for his good will and make the settlement offer. Send a handwritten note to the Doctor personally (not the offic manager). Send it Priority Mail, so you can make sure it is delivered. Doctors hate bad publicity.
Note, too, if this is a hospital bill, there are different things you should be considering, especially if there was no insurance involved.