This paper investigates the use of general bases with fixed poles for the purposes of robust estimation. These bases, which generalise the common FIR, Laguerre and two-parameter Kautz ones, are shown to be Fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied. It is also shown that, by using a min-max criterion, these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified. The key idea facilitating this analysis is to re-parameterise the chosen model structures into a new one with equivalent fixed poles, but for which the basis functions are orthonormal in H-2(D).