This paper introduces an iterative algorithm for designing IIR digital filters that minimize a complex approximation error in an Lp sense. The algorithm combines ideas that have proven successful in the similar problem of Lp FIR filter design. We use iterative prefiltering techniques common in applications such as parameter estimation together with an Iterative Reweighted Least Squares (IRLS) method. The result is a double iterative approach that generates IIR filters of arbitrary magnitude and phase response and arbitrary numerator and denominator orders. Such filters can be used in a variety of applications in which the typical L2 or Minimax error criteria might not be suitable.