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This paper introduces an optimality criterion for mixed-level supersaturated designs, called E (χ2), which covers E (s2) for two-level designs and ave (χ2) for symmetrical designs as two special cases. Some lower bounds of E (χ2) are obtained. Furthermore, it is shown that the E (χ2) criterion coincides with other existing criteria for nonregular mixed-level fractional factorial designs, which include minimum moment aberration, generalized minimum aberration, discrete uniformity and design efficiency. Several classes of E (χ2)-optimal mixed-level supersaturated designs from saturated orthogonal arrays are given. © 2005 Elsevier B.V. All rights reserved.