As a sequel to [arch04], the position of the maximum in a geometrically distributed sample is investigated. Samples of length n are considered, where the maximum is required to be in the first d positions. The probability that the maximum occurs in the first d positions is sought for d dependent on n (as opposed to d fixed in [arch04]). Two scenarios are discussed. The first is when d=αn for 0 < α≤1, where Mellin transforms are used to obtain the asymptotic results. The second is when 1 ≤d = o(n).