We consider a set of accounts written by two university lecturers describing incidents that took place during their first-year Calculus modules. Analysis of these accounts revealed that the lecturers had to make some difficult decisions while teaching. These situations sometimes involved choices between two or more alternatives each of which had disadvantages. We labelled these choices ‘dilemmas’. Here we present and discuss the three most common types of dilemma evident from our data: namely, balancing good practice in teaching with students’ feeling of discomfort; balancing the needs of students with different backgrounds; balancing time constraints and active participation by students.