Many confounded factorial arrangements have the property of obtaining the same precision for any component of a particular main effect or interaction. A procedure for recovery of inter-block information developed by the author (Ann. Math. Statist 1964) is applied to such designs to obtain combined estimators having smaller variance than the corresponding intra-block estimators for all values of the inter and intrablock variances. The procedure has been illustrated for a confounded factorial arrangement of the above type.