Since ID is a subspecialty of Internal Medicine, the following rules only pertain to Internal Medicine as the entry point into the ICU (as opposed to anesthesiology, EM, etc.):

1.) A 2-year CCM-only fellowship can be done by anyone who has finished internal medicine residency. 

2.) A 1-year CCM-only fellowship can be done by anyone who has finished any prior internal medicine subspecialty fellowship. 

3.) You can only sit for the CCM board exam after a.) finishing a  2-year CCM fellowship or b.)  finishing a 1-year CCM fellowship AND passing the board exam of your prior subspecialty first.

Because of the above requirements for the 1-year fellowships, many programs may have you applying twice, once for each fellowship.