To give you a straight answer to the question: No. Not that I know of. It's a tall order to sum up exactly the meaning of two adjectives in one word.
I'm not totally happy with this, but you might try the word "utilitarian." A person with a utilitarian mindset is more concerned with the fact that a thing works. So there is some significant overlap with pragmatism. Also, it seems to me that if someone has a utilitarian mindset he or she would generally do things as efficiently as possible. Such a person is concerned about usefulness, and generally, inefficient things are less useful. Such a person would not be concerned about doing things the "traditional way" unless, of course, it worked best. And, as Smock points out in his comment, the traditional way sometimes is the most efficient way.
Again, I am not totally happy with this, especially regarding sufficient overlap in meaning with the word efficiency. Check it out and see what everyone else suggests.