Contingent Convertibles ("CoCos") are contingent capital instruments which convert into shares, or have a principal write down, if a trigger event takes place. CoCos exhibit the undesirable so-called "death-spiral effect": by actively hedging the equity risk, investors can (unintentionally) force the conversion by making the share price deteriorate and eventually trigger the conversion.In this paper we introduce and analyse Coupon Cancellable CoCos ("CoCa CoCos"), a new type of CoCo where coupons can be cancelled during the lifetime of the note. We provide closed form pricing formulas for CoCa CoCos, and we show that death-spiral effect is reduced.