Abstract
In estimating a finite population proportion of people bearing a stigmatizing characteristic Warner's (1965) Randomized Response(RR) device is well-known when the complementary characteristic is supposedly innocuous. But when both may be sensitive Simmons' Unrelated(URL, in brief) Model RR device is well-known as a feasible alternative. Both devices generate RR's by Bernoullian trials recording data on a match or mis-match of a respondent's true feature and the feature marked on a randomly chosen card drawn from a box placed in front of the person. A recently reported `alternative' device records instead the first occurrence of a `match' in repeatedly drawn cards from the box with replacement. This artifice fails with URL model. An amended procedure is presented demonstrating its advantages.