Traditional priority schemes reduce delays for some by increasing those of others. Yet, this might not be a necessity. Several works published over the last two decades have shown for a stylized set-up with homogeneous users that dynamic priority scheme may be Pareto improving. They induce socially efficient departure time adjustments similarly to a coarse congestion pricing strategy, but without any financial transaction. This paper improves realism by introducing two types of heterogeneity: in schedule preferences and in capacity usage. The consequences of heterogeneity in schedule preferences are mostly negative. When users have different levels of flexibility, prioritizing randomly selected users deteriorates the departing order. As a consequence, the cost savings are smaller than in the homogeneous case, and some users are worse off. A similar effect exists when users have different preferred arrival times, but there the relative cost savings may actually be larger, due to the complete avoidance of queues for priority users. The consequences of heterogeneous capacity usages on the other hand are positive, as capacity usage (e.g. vehicle occupancy) can be used as selection criterion. This generates further operational benefits, as well as a potential mode shift, which both contribute to a better distribution of benefits. Under favorable circumstances, this may even restore a Pareto improvement. Overall, dynamic priority appears as a realistic alternative to congestion pricing, scoring well both in terms of efficiency and social acceptability.