Many countries promote choice for schools. How choice is actually implemented greatly varies across countries and school districts and is often hotly debated by stakeholders. A cornerstone of this debate is the choice of the algorithm used to allocate students to schools, when capacity is limited. A classic trade-off that school districts face when deciding which algorithm to use to match students to schools is that it is not possible to always respect both priorities and preferences. The student-proposing deferred acceptance algorithm respects priorities (fairness) but can lead to inefficient allocations. The top trading cycle algorithm respects preferences (efficiency) but may violate priorities. We identify a new condition on school choice markets under which both algorithms yield the same allocation. Such condition is natural as priorities are often the reflection of what school districts view as legitimate preferences. We quantify through simulations the extent to which our condition extends the known range of environments where fairness and efficiency do not conflict.