This paper studies continuous-time system model sets that are spanned by fixed pole orthonormal bases. The nature of these bases is such as to generalise the well known Laguerre and two--parameter Kautz bases. The contribution of the paper is to establish that the obtained model sets are complete in all of the Hardy spaces Hp provided that a mild condition on the choice of basis poles is satisfied. A characterisation of how modelling accuracy is affected by pole choice, as well as an application example of flexible structure modelling are also provided.