The idea that an individual has a 'right not to know' genetic information about himself or herself is entrenched in both the policy sphere and the genetic counselling ethos. In this paper, I interrogate this idea of a 'right not to know', questioning particularly its status as a right. I identify the conception of rights that seems to underlie the posited 'right not to know' as a conception of rights in which they are prioritised non-outweighable interests. Turning to a series of hypothetical situations in which the 'right not to know' is invoked, I argue that the 'right not to know' is not a right consistent with such a conception. The 'right not to know' can only exist in a framework of rights in which they lack significant moral weight. Thus, considering the gravity of rights in popular understanding, I suggest caution in continuing use of the phrase 'right not to know' in the context of genetic testing. This investigation suggests that structuring the debate around genetic ignorance in terms of the 'right not to know' is not conducive to moving forward ethical thinking in this area.