A three-phase "task-first" lesson structure is frequently suggested when teaching mathematics through inquiry. We investigate how secondary school teachers of mathematics structure their inquiry lessons and examine how and why they deviate from a "task-first" structure. We present detailed lesson observation data from three teachers participating in a year-long professional development programme focused on inquiry teaching. We track the developing structure of these teachers' inquiry lessons through minute-by-minute lesson analysis, describe how their lesson structures altered over time and explore why. Our data show that contextual constraints may explain why teachers departed from the "task-first" lesson structure. In their inquiry teaching, two of the teachers adopted more scaffolded approaches, including the use of a sequence of smaller sub-tasks and teacher interventions. We argue that these modifications to a "task-first" lesson structure are legitimate ways to support student learning through inquiry; indeed, that they may offer some advantages for inquiry teaching.