1. Pertaining to the ability to capture and to hold a person's attention: The story Mrs. Smart was reading to her class was so compellable that all the children were listening very carefully.
2. Regarding the capability of causing someone to believe or to agree with something: He made a compellable and convincing argument so that everyone in the room approved of it.
3. Referring to something which makes a person feel that something must be done: The reasons in the petition for a new playground for the children made quite a compellable case, so all the parents signed it immediately and hoped that it would be built soon!