Method for determining a target measured value, which comprises a visco sity of a medium or a viscosity-dependent variable, of a medium flowing through a measuring tube on the basis of preliminary damping measured values of at least one oscillation mode of the measuring tube, the damping being dependent on the vis cosity of the medium and having a cross-sensitivity to the flow velocity of the medium, the method comprising: Excitation of oscillations of at least one oscillation mode; acquiring a sequence of preliminary measured damping values (110; 210) for the at least one vibration mode of the measuring tube; and Calculate target measured values (140; 240); that a correction of the influence of the cross-sensitivity of the damping on the flow velocity of the medium is carried out by determining (130; 230), on the basis of the preliminary measured damping values, adjusted measured damping values which correspond to the damping in a non-flowing medium, and the target measured values are determined on the basis of the adjusted measured damping values, or a correction of the influence of the cross-sensitivity of the damping on the flow velocity of the medium is carried out by determining (112; 114) preliminary intermediate values of a damping-dependent variable on the basis of the preliminary damping measured values, determining (132; 134) adjusted intermediate values which correspond to the intermediate values for a non-flowing medium, and determining the target measured values on the basis of the adjusted intermediate values, characterized in that the cross-sensitivity of the attenuation to the flow velocity above a critical velocity value causes the attenuation to increase with the flow velocity, and the fluctuation of the preliminary attenuation measurement values increases with the flow velocity, wherein the correction of the influence of the cross-sensitivity is carried out on the basis of the flow tuation of the preliminary measured attenuation values or the preliminary intermediate values and/or on the basis of a function which depends on a flow parameter of the medium, wherein the flow parameter comprises, in particular, a preliminary value of the mass flow rate, the volume flow rate, the Reynolds number or the flow velocity. Excitation of oscillations of at least one oscillation mode; acquiring a sequence of preliminary measured damping values (110; 210) for the at least one vibration mode of the measuring tube; and Calculate target measured values (140; 240); that a correction of the influence of the cross-sensitivity of the damping on the flow velocity of the medium is carried out by determining (130; 230), on the basis of the preliminary measured damping values, adjusted measured damping values which correspond to the damping in a non-flowing medium, and the target measured values are determined on the basis of the adjusted measured damping values, or a correction of the influence of the cross-sensitivity of the damping on the flow velocity of the medium is carried out by determining (112; 114) preliminary intermediate values of a damping-dependent variable on the basis of the preliminary damping measured values, determining (132; 134) adjusted intermediate values which correspond to the intermediate values for a non-flowing medium, and determining the target measured values on the basis of the adjusted intermediate values, characterized in that the cross-sensitivity of the attenuation to the flow velocity above a critical velocity value causes the attenuation to increase with the flow velocity, and the fluctuation of the preliminary attenuation measurement values increases with the flow velocity, wherein the correction of the influence of the cross-sensitivity is carried out on the basis of the flow tuation of the preliminary measured attenuation values or the preliminary intermediate values and/or on the basis of a function which depends on a flow parameter of the medium, wherein the flow parameter comprises, in particular, a preliminary value of the mass flow rate, the volume flow rate, the Reynolds number or the flow velocity.