Two modifications of trochoidal electron analysers are proposed. The first uses the non-uniform electric field at the half-plane electrode edge. The optimum conditions of electron transmission are determined from the equations of motion. The analytic expressions for similarity laws are derived in a drift approximation. The second modification uses a geometry close to that of a conventional trochoidal monochromator. Two half-planes with a narrow strip in a gap between them are used instead of one solid plane electrode. In this case, the optimum conditions are found numerically and plotted graphically. In comparison with the non-uniform field analysers developed previously, the analysers being proposed possess an important advantage, namely the simple shape of their electrodes, their improved performances appearing quite similar.