With the increasing penetration of converter-interfaced generation, it would be advantageous to specify local grid-connectivity criteria to ensure small-signal stability of the interconnected system, rather than carrying out centralized stability studies every time the connection of a new device is contemplated. Passivity of the device admittance, which is an example of a local criterion, has been used previously to avoid resonances between converter-interfaced systems and the lightly damped oscillatory modes of the network, but it is unsuitable in general due to the conservative nature of passivity. Therefore, a composite set of criteria are proposed in this paper, which include time-scale separation (slow-fast clustering) constraints on the transient behaviour, and distinct passivity constraints for the slow and fast clusters. The application of these criteria is demonstrated using a case study.