This paper examines the precision of complex viscosity measurements in the constant stress and constant strain modes. A Bohlin Controlled Stress Melt Rheometer was used to make the measurements, which cover a stress range of 400 to 3227 Pa and a frequency range of 0.01 to 30 hertz. In principle, oscillation in the linear region should give the same values regardless of how it is done. In reality, various measurement modes exhibit different precision. A wide range of parameters encompassing three decades in complex viscosity and over three decades in frequency are considered. Contrasting frequency dependence, i.e., shear-thinning and Newtonian plateau, are also considered. Constant stress measurements are found to provide improved precision at lower frequencies, while constant strain measurements provide improved precision at higher frequencies. This is significant because low frequency data are often used to estimate the zero-shear viscosity, which correlates with the weight-average molecular weight. The "between-sample" and "within-sample" components of the total variation are examined separately for poly(dimethyl siloxane) and polyethylene. To do this for polyethylene, a new technique (moving range average) had to be used. Initial attempts at modeling are discussed. The discussion is limited to isotropic polymeric melts. This paper provides guidance in determining the most appropriate way to perform oscillation.