A not too uncommon type of compulsion in people suffering from
OCD, which consists of the OCDer trying to discontinue the thought that is the
obsession's subject away in one of several ways.
One such way is thought stopping, where the OCDer attempts to halt their thinking so that they wouldn't have to think the obsessive thought.
Another way is thought skipping, where the OCDer tries to launch into a different thought before the obsessive thought generates anxiety. This is possibly the most common form of mental compulsion.
Thought negating is also a very common mental compulsion, where the OCDer tries to think a thought that they consider to be contradictory to the obsessive thought. For instance, obsessions about harming a loved one might be followed by the mental compulsion of thinking of loving them.
Rationalization is probably the most interesting and exhausting form of mental compulsion. The OCDer would try to frantically rationalize the subject of obsession in such a way that they feel it should no longer pose a threat. For instance, obsessing about confrontation with a certain person might be followed by trying to find rational and logical explanations for why that person doesn't pose a threat.
One of the main problems with mental compulsions is that they very often work very well to prevent the anxiety and relieve the OCDer, while at the same time relate greater and greater significance to the subject of the obsession. This is a mechanical and subconscious side-effect. The more the OCDer actively works to "solve" the obsession, the more "urgent" and "threatening" the mind considers it to be, the more recurrent the obsession gets.
One of the skills that cognitive-behavioal therapists attempt to teach the patient is how to refrain from executing those mental compulsions (which is a rather simple practice), but rather letting the obsession hang indefinitely. As the patient learns to do this, the easier it is for the brain to habituate the obsessive thought, which results in a lessening of the anxiety generated by this thought.
Possibly the greatest difficulty in getting the patient to habituate their obsessions is by getting them to believe that the obsession can indeed be neutralized.