A Stackelberg game framework is presented to choose the detector tuning for a general detector class under stealthy sensor attacks. In this framework, the defender acts as a leader and chooses a detector tuning, while the attacker will follow with a stealthy attack adjusted to this tuning. The tuning chosen is optimal with respect to the cost induced by the false alarms and the attack impact. We can show that under some practical assumptions the Stackelberg game always has a solution and we state two different sufficient conditions for the uniqueness of the solution. Interestingly, these conditions show that the attack impact does not have to be a convex function. An illustrative attack scenario of a false-data injection attack shows how one can use the Stackelberg game to find the optimal detector tuning.