The stability of haptic simulation systems has been studied for a safer interaction with virtual environments. In this work, the passivity, uncoupled stability, and fidelity of such systems are analyzed when a viscoelastic virtual environment is implemented using a general discretization method that can also represent methods such as backward difference, Tustin, and zero-order-hold. Dimensionless parametrization and rational delay are considered for device independent analysis. Aiming at expanding the virtual environment dynamic range, equations to find optimum damping values for maximize stiffness are derived and it is shown that by tuning the parameters for a customized discretization method, the virtual environment dynamic range will supersede the ranges offered by methods such as backward difference, Tustin and zero-order-hold. It is also shown that minimum time delay is required for stable Tustin implementation and that specific delay ranges must be avoided. The proposed discretization method is numerically and experimentally evaluated.