Simulations and analysis of power-electronic-based systems are conventionally done using detailed switching models of power-electronic converters that are available in many electromagnetic transient (EMT) simulation programs. Although being accurate, such detailed models typically require small time-steps for accurate detection and handling of switching events, which makes them computationally expensive. Recently, a parametric average-value modeling (PAVM) approach has been developed for system-level modeling and fast simulations of line-commutated rectifiers (LCRs) including several selected ac harmonics. In this paper, a new hybrid parametric methodology is presented, which has the capability of operating at large time-steps while including the details of the ac- and dc-side variables similar to the detailed switching models (but without the need for locating switching events, i.e., zero crossings), or operating as an average-value model. Extensive simulation studies demonstrate advantageous numerical efficiency and accuracy of the proposed hybrid parametric AVM/detailed model compared to the previous PAVMs as well as the detailed switching models of LCRs when using large time-steps for system-level studies.