The sinuous antenna is a bidirectional, frequency independent antenna. To achieve unidirectionality, a lossy cavity is employed, but at the cost of efficiency. This paper proposes a minimally lossy cavity that improves the efficiency performance. To compensate for increased mismatch loss from the minimally loss cavity, the sinuous element is non-complimentary near the feed to improve the impedance match. At larger diameters, the sinuous is complementary to maintain the frequency independent performance of the sinuous.