Promoting Integrity at the Classroom Level:
Don't Rush Students
Students are more likely to cheat if they do not feel they have adequate time to successfully complete an assignment in the time permitted.
Help students management their time by breaking an assignment into parts or requiring reflection.
You can also monitor your classes to see when students most likely do their work. For example, in my online classes, I allow weekly discussions to run 9 days because I have learned that online students--especially those who have full-time jobs--plan to use their weekends for course work. (On most weekends, students could work in one or both of two weekly discussions.)
Finally, if you are able to develop a relationship with your students, those who do get into a bind are more likely to come to you discuss options than they are to cheat. Holding conferences is both a good way to build a relationship with students while also monitoring their progress.