Experimenters sometimes impose on the animals allocated to different treatments the condition that treatment means in respect of some preliminary measurement, believed to be correlated with the measurement that is to be used in assessment of results, shall be approximately equal. Such balance may be used in completely randomized or randomized block designs. The expected variance of treatment means for these designs and for the corresponding randomized designs are compared. Three major criticisms of the balanced designs emerge: difficulty of objective allocation, temptation to omit the necessary covariance analysis, and smallness of any gain in precision. The disadvantages seem far to outweigh the advantages, and such designs should not be used unless special circumstances dictate their advisability. The possibility of using Latin square and allied designs as alternatives to the type of balance discussed is briefly mentioned. When there is anything to be gained by balance, these designs avoid the theoretical objections and will usually have almost equal merits.