Testwiseness is defined as the set of cognitive strategies used by a student that is intended to improve his or her score on a test regardless of the test's subject matter. Questions with elements that may be affected by testwiseness are common in physics assessments, even in those which have been extensively validated and widely used as evaluation tools in physics education research. The potential effect of several elements of testwiseness were analyzed for questions in the Force Concept Inventory (FCI) and Conceptual Survey on Electricity and Magnetism that contain distractors that are predicted to be influenced by testwiseness. This analysis was performed using data sets collected between fall 2001 and spring 2014 at one midwestern U.S. university (including over 9500 students) and between Spring 2011 and Spring 2015 at a second eastern U.S. university (including over 2500 students). Student avoidance of "none of the above" or "zero" distractors was statistically significant. The effect of the position of a distractor on its likelihood to be selected was also significant. The effects of several potential positive and negative testwiseness effects on student scores were also examined by developing two modified versions of the FCI designed to include additional elements related to testwiseness; testwiseness produced little effect post-instruction in student performance on the modified instruments.