The extreme points of the (ε, 0)-differential privacy polytope have been studied in prior work [9]–[11]. No such results exist for the (ε,δ)-differential privacy polytope for δ > 0. In this work, we highlight the challenges involved in this setting by studying the special case of the (0,δ)-differential privacy polytope with input [k] and output [m]. We characterise all extreme points for arbitrary k and m ≤ 3. We show that such a characterisation is elusive for m ≥ 4 by demonstrating examples of extreme channels that defy some natural conjectures.