Minimum bias estimation was suggested as an alternative to least squares for polynomial tits by Karson. Manson, and Hader (1969). To use this alternative, a combination of least squares estimates of coefficients of the model order fitted, and of the additional model order whose bias is being guarded against, needs to be calculated. Individual estimation of the higher-order coefhcients is usually not necessary, and the question of finding parsimonious designs that provide only those combinations of estimated coefficients that are needed is explored. Some specific types of designs are suggested, including a new type of second-order rotatable design consisting of combinations (inkdimensions) of two-dimensional equiradial point sets.