punctilious

People described as punctilious do things (or require things to be done) exactly according to the rules or in a particular or traditional way—the one they consider proper.

Such people may be described as strict, rigid, inflexible, or fussy. Strict implies close adherence to rules. Rigid and inflexible imply that a person isn’t willing to change the way they do things. Fussy is a more negative way of saying someone is particular—that they want things done in an exact way.

All of these words are less formal than punctilious. An even less formal but more negative term is persnickety, which can suggest that someone is annoyingly particular, often in a way that’s snobby. A more formal synonym that can mean just about the same thing is scrupulous, but scrupulous is more commonly used to mean principled or devoted to doing what is right.