We study in the laboratory, a variant of the house allocation with existing tenants problem where agents are partitioned into tiers with different privileges. Members of higher tiers receive their allocation before those in lower tiers and can also take the endowment of a member of a lower tier if they wish to. In this tiered environment, we evaluate the performance of the modified versions of three well-known mechanisms - the Top Trading Cycle (TTC), the Gale-Shapley (GS) and the Random Serial Dictatorship (RSD). For all three mechanisms, we find low rates of participation (around 40%), high rates of truthtelling conditional on participation (around 90%) and efficiency levels that are high (above 90%) but below full efficiency. Also, of the three novelties introduced in our experiment tiered structure, multiple matches and known priority queue- only the last one has an impact on choices, with subjects being significantly more likely to participate the higher their position in the queue. Finally, the majority of subjects who do not play according to the theory still follow discernible patterns of participation and preference revelation.