A fuse for a projectile has a primary firing assembly and a secondary firing assembly. The secondary firing assembly, which is separated from the primary firing assembly by a barrier, has a firing relay with a relay explosive in a sleeve component and a firing booster. When using insensitive explosive for the secondary firing assembly, little energy should be lost in the relay from the primary to the secondary firing assembly, with enhanced safety against inadvertent firing in the secondary firing assembly. For that purpose, the sleeve component forms a gas-tight seal for the secondary firing assembly with respect to the primary firing assembly.