Despite being >10 Myr, there are ∼10 debris discs with as much CO gas as in protoplanetary discs. Such discs have been assumed to be ‘hybrid’, i.e. with secondary dust but primordial gas. Here, we show that both the dust and gas in such systems could instead be secondary, with the high CO content caused by accumulation of neutral carbon (C0) that shields CO from photodissociating; i.e. these could be ‘shielded secondary discs’. New ALMA observations are presented of HD131835 that detect ∼3 × 10−3 M⊕ of C0, the majority 40–200 au from the star, in sufficient quantity to shield the previously detected CO. A simple semi-analytic model for the evolution of CO, C, and O originating in a volatile-rich planetesimal belt shows how CO shielding becomes important when the viscous evolution is slow (low α parameter) and/or the CO production rate is high. Shielding by C0 may also cause the CO content to reach levels at which CO self-shields, and the gas disc may become massive enough to affect the dust evolution. Application to the HD 131835 observations shows these can be explained if α ∼ 10−3; an inner cavity in C0 and CO may also mean the system has yet to reach steady state. Application to other debris discs with high CO content finds general agreement for α = 10−3 to 0.1. The shielded secondary nature of these gas discs can be tested by searching for C0, as well as CN, N2, and CH+, which are also expected to be shielded by C0.