Fractional factorial designs are widely used in industry and agriculture. Over the years much research work has been done to study these designs. Foldover fractional factorial designs can de-alias effects of interest so that the effects can be estimated without ambiguities. We consider optimal foldover designs using general minimum lower-order confounding criterion. Some Properties of such designs are investigated. A catalogue of 16- and 32-run optimal foldover designs is constructed and tabulated for practical use. A comparison is made between the general minimum lower-order confounding optimal foldover designs and other optimal foldover designs obtained using minimum aberration and clear effect criteria.