This paper deals with estimation of reliability parameters when life testing is conducted at stress levels above that which would normally be applied in standard usage. A range of stress for testing is prescribed, and a two-parameter Weibull model for failure times is assumed. The logarithm of the Weibull scale parameter is assumed to be a polynomial function of known degree k of the reciprocal of stress level. The Weibull shape parameter is assumed to be independent of stress level. The problem considered is that of determining the design for obtaining the least-squares-curve intercept with minimum variance at the nominal testing level. The design obtained specifies the number and location of stress levels in the prescribed range at which the life tests will be conducted and proportion of the total sample of specified size to be randomly allocated to each testing level.