Objective. Polycrystalline mercuric iodide photoconductive converters fabricated using particle-in-binder techniques (PIB HgI2) provide significantly more detected charge per x-ray interaction than from a-Se and CsI:Tl converters commonly used with active matrix flat-panel imagers (AMFPIs). This enhanced sensitivity makes PIB HgI2 an interesting candidate for applications involving low x-ray exposures—since the relatively high levels of additive electronic noise exhibited by AMFPIs incorporating a-Se and CsI:Tl reduce detective quantum efficiency (DQE) performance under such conditions. A theoretical study is reported on an approach for addressing a major challenge impeding practical use of PIB HgI2 converters—the high lag exhibited by the material (over 10%) which would lead to undesirable image artifacts in applications involving acquisition of consecutive images such as digital breast tomosynthesis. Approach. Charge transport modeling accounting for the trapping and release of holes (thought to be the primary contributor to lag) was used to examine signal properties, including lag, of pillar-supported Frisch grids embedded in the photoconductor for 100 μm pitch AMFPI pixels. Performance was examined as a function of electrode voltage, grid pitch (center-to-center distance between neighboring grid wires) and the ratio of grid wire width to grid pitch. Main results. Optimum grid designs maximizing suppression of signal generated by hole transport, without significantly affecting the total signal due to electron and hole transport, were identified and MTF was determined. For the most favorable designs, additional modeling was used to determine DQE. The results indicate that, through judicious choice of grid design and operational conditions, first frame lag can be significantly reduced to below 1%—less than the low levels exhibited by a-Se. DQE performance is shown to be largely maintained as exposure decreases—which should help to maintain good image quality. Significance. Substantial reduction of lag in PIB HgI2 converters via incorporation of Frisch grids has been demonstrated through modeling.