Ideally the experimenter would like to use treatment design to minimize both variance and bias problems in estimating yield from fertilizer application. Selecting a treatment design for variance considerations will not give a minimum bias design. Since different criteria of optimality lead to different designs, the most appropriate criterion under a given set of circumstances will be determined by the specific use that is made of the data generated by the design, e.g., in fertilizer use studies the slope of the estimated response surface near the economic optimal could be most important. For the quadratic polynomial estimating function and a square root true function in two variables, treatment designs are compared empirically using several variance criteria in addition to a volume concept of bias. In general, bias is decreased by restricting the treatment combinations to an area of the factor space not including the boundaries. Increased variance of various estimated parameters may be controlled through replication of the relatively small treatment designs needed for bias considerations.30