The Monte Carlo method applied to the circuit tolerance analysis problem has the attraction of insensitivity to the number of toleranced components, but is computationally expensive. However, its efficiency can be improved by exploiting variance reduction techniques. The paper describes a novel application and development of one such technique, namely the control variate method. The paper outlines the standard Monte Carlo method and introduces the control variate procedure. The estimation of circuit properties such as yield, yield sensitivities and moments of performance function distributions are described. The control variate method requires the introduction of a circuit which we call the shadow model, whose performance approximates that of the circuit under consideration, but is much cheaper to analyse. We present experimental results for a particular circuit example and its shadow model and make suggestions for the general construction of shadow models.