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Sometimes, there are legitimate reasons why you didn’t pay a bill. If a contractor refused to finish a job or did a poor job, then you may have refused payment, but the non-payment may still count against you on your credit report. If there are any unusual circumstances surrounding your credit report that may affect your credit rating - such as a case of identity theft - you can ask that a note be attached to your credit report to explain the problem.
Some lenders will pay attention to this and some will not, but it is a better solution than nothing at all. Such a note will not affect your credit score but will affect your credit report. More importantly, it leaves a paper trail of the problem that lenders can look at if they choose.