We present an optimized solution to the problem of membrane impedance estimation when a patch-clamped cell is stimulated by a dual-frequency, sinusoidal excitation. The complete data set of raw whole-cell current samples is typically reduced, via digital lock-in detection, to measurements of the complex cell model admittance at the two stimulus frequencies. We describe a statistical model of both data sets and demonstrate that the admittance data adequately represent the essential features obtained from the raw data. The parameter estimates obtained by a nonlinear weighted least-squares solution (NWLS), which under normal recording conditions is equivalent to the maximum likelihood solution, essentially obtain the theoretical lower bound on variance established by the Cramér-Rao bound. Our software implementation of the NWLS solution produces estimates of the cell model parameters that are less noisy than other dual-frequency systems. Our system can be used 1) to measure slow changes in membrane capacitance-in the face of large, slow changes in membrane resistance, 2) to detect with confidence capacitance changes expected from the exocytosis of moderate-sized dense core granules, and 3) to reduce the cross-talk between transient changes in membrane conductance and membrane capacitance.