So I think the reason why some of the posters (myself included) are a bit confused, is because of your wording of your question. When you say "Moderate Complexity", this usually explains the overall MDM, and does not explain History or Examination.
If you are looking for help to code the correct E/M level, then I highly recommend you study the CMS E/M guidelines first, and then look at the different E/M audit tools out there. There are plenty to choose from if you do a search. If your organization does not have an E/M audit tool, then I would suggest creating one, based on the guidelines and support available.
Let me give you a list of links that should guide you in the right direction:
CMS E/M guidelines
AAPC E/M audit tool
E/M University (Free section)
I would start studying these resources and then go from there.
As far as your denials go, they could be denied either based on the E/M level or patient status (New vs. Established). I would check both and reaudit them to see if you have grounds enough for an appeal.
Good luck!