A novel mixed randomised/deterministic method for fixed-order controller design is proposed for discrete-time single-input single-output plants. It is based on the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are then projected onto the affine set of closed-loop characteristic polynomials and the stable line segments in the controller parameter space are determined. A novel approach is proposed for global and local optimisation over reflection segment bunches on the basis of the weighted sum of absolute values of reflection coefficients.