Experiments have demonstrated the possibility of increasing the resolving power of determining the point gamma-radiation source direction in the precision method. The work involved reducing the step of the angle of rotation of an asymmetric absorber and shifting the detector relative to the maximum-minimum absorber thickness boundary. The ¹³⁷Cs gamma-radiation source direction was determined within the angles of the maximum and minimum thickness boundaries of the asymmetric absorber. The detector position was investigated for the maximum thickness of the asymmetric absorber on the boundary between the maximum and minimum thickness, and for the minimum thickness. The optimal position of the detector was found for the asymmetric absorber boundary, enabling to determine the maximum count rate in the gamma source direction. A specific position of the detector enables observing an increasing gamma radiation scattering over the copper-lead surface. The experiment used absorbers with spectrometric telluride-cadmium detectors. Information from the detectors was output to four multichannel gamma-radiation impulse analysers, which operated simultaneously in the spectrometer mode.