Tasks showing up as critical that are not

We are trying to manage the critical path on a project and there are some tasks that the project manager does not want on critical path. The first task that we tried to get off of critcal path proved to be a problem. We removed the predecessors to the task and it remained critical. We removed the successors to the task and it remained critical. It is unconstrained, un-linked, stand alone, only 7 days long in a several month project, and still remains critical. And the total slack remains at 0 no matter what we do.
What am I doing wrong?