A quantitative upper hound is established which defines the extent to which a minimum-order reduced-order non-adaptive observer may be rendered insensitive to parameter variations. That upper bound depends on the number of measurements and the location of questionable parameters within the system matrices. An integral squared error objective function is explicitly solved. That objective function may be used to assess the sensitivity of the system to parameter errors. A numerical example is presented for a continuous observer. The results are extended to the discrete ease.