In this paper we show that the maximum likelihood estimators of LD50 and the scale parameter in the logistic case are equivalent to the Spearman-Karber type of estimators, when the subsample sizes at each dose level are equal. We derive a simple expression for the asymptotic variance-covariance matrix of the estimators. We also obtain correction terms to the bias and the variance of the Spearman-Karber estimator of LD50. Using these we construct sequential fixed-width and risk-efficient procedures for LD50. Numerical calculations show that these procedures are simple to carry out and stop at fewer dose levels than those proposed earlier by Nanthakumar and Govindarajulu (1994, 1999).