Professors who teach introductory astronomy to students not majoring in science desire them to comprehend the concepts and theories that form the basis of the science. They are usually less concerned about the myriad of detailed facts and information that accompanies the science. As such, professors prefer to test the students for such comprehension. The multiple choice format for examinations is often excluded since it appears to focus only upon factual information. This paper proposes to show that the multiple choice format can be used to create non-trivial examinations that test for higher-order thinking. The paper shows, with numerous examples, how to design such questions within the didactic framework of Bloom's taxonomy. Following a discussion of how the taxonomy relates to goals and objectives in teaching astronomy, the paper proceeds to focus upon each of the taxonomic categories with examples of sophisticated questions about specific astronomical concepts. The goal is to explicate the design theory so that instructors can create unlimited numbers of questions for their own courses. As such, it is not a research paper but, rather, one to provide working instructors with helpful hints for improving their testing. Included at the end of the paper is an algorithm for the construction of a grade curve, and some discussion of using the statistical analysis of the examination questions to evaluate the performance of individual students and to improve the test questions themselves. (Contains 3 tables and 1 figure.)