A new estimator of the scale parameter as an optimum linear combination of absolute values of order statistics in logistic distribution with known location parameter (without loss of generality assumed to be zero) from complete and type II censored samples is obtained and is named as optimum unbiased absolute estimator (OUAE), The new estimator is compared with the corresponding best linear unbiased estimator (BLUE) and is found to be more efficient than BLUE. Next we derive the BLUE and OUAE based on k-optimally selected order statistics and observed that BLUE or OUAE based on 5 optimally selected order statistics would give an estimator with efficiency of more than 92%.