We consider identification (in both the time domain, for suitable choices of inputs, and the frequency domain) using a deterministic formulation that is less conservative than the usual worst-case approach, in that it allows for a certain number of outliers. Two new identification methods, the Orlicz and The Top K method, respectively, are proposed and analysed. Theoretical H-infinity error bounds for the identified models are provided, and the proposed methods are illustrated by a numerical example.