The word "specific" is a great synonym for "not general". The term refers to a specific item or characteristic, rather than a broad or general category. Another synonym for "not general" is "particular", which also pertains to a specific or individual object or situation. "Narrow" is another word that can be used to describe something that is not broad or general in scope. And for a more formal tone, "circumscribed" can also be used to convey the idea of something that is limited in scope. Overall, all these synonyms are useful in describing things that are not general or all-encompassing.