This paper investigates how rent control affects mobility in the Danish housing market. We apply a proportional hazard duration model, that encompasses both the presence of left truncated tenancy durations, right censored observations and allows for a very flexible specification of the time dependency of the hazard rate. Tenancy mobility is severely reduced by rent control. For a typical household in the private rental sector tenancy duration is found to be more than six years longer if the apartment belongs to the 10% most regulated units than if it belongs to the 10% least regulated units.