Digital filters based on stochastic computation have recently gained considerable attention because the stochastic computation attains significant reduction of hardware complexity of digital filters compared with the classical deterministic binary computation-based filters. For stochastic IIR filters, Liu and Parhi proposed an elegant method that achieves high precision by means of the normalized state-space lattice structure. This paper extends the result and presents stochastic state-space IIR filters with higher precision than the conventional method. Instead of using the normalized lattice structure, our method makes use of the minimum roundoff noise structure in realizing stochastic state-space filters, leading to further improvement of arithmetic precision of IIR filtering compared with the conventional method. Experimental results show that our method gives higher signal-to-error ratio at the filter outputs than the conventional method.