  Dispersion relations for S-matrices and CFT correlators translate UV
consistency into bounds on IR observables. In this note, we construct
dispersive sum rules for 1D CFTs. We use them to prove bounds on
higher-derivative couplings in weakly-coupled non-gravitational EFTs in
AdS$_2$. At the leading order in the bulk-point limit, the bounds agree with
the flat-space result. We compute the leading universal effect of finite AdS
radius on the bounds. Along the way, we give an explicit formula for anomalous
dimensions in general higher-derivative contact Witten diagrams in AdS$_2$.
