The circular ring transaxial positron camera developed earlier was refitted with a new dichotomic sampling scheme and aperture collimators on the detector array to improve the sampling and the overall system resolution. The z-axis slice thickness collimators were also limited to 1 cm, which corresponds to a slice thickness of 0.5 cm FWHM. Two different types of aperture collimators were adopted for high resolution (HR) and very high resolution (VHR) imaging, respectively. In HR mode a resolution of 6.5 mm FWHM was obtained without appreciable degradation of overall sensitivity, which represents a threefold improvement in resolution over the original system. In phantom studies with HR mode a sensitivity of 4500 counts s-1 muCi-1 cm-3 was obtained for a 20 cm diameter uniform phantom filled with water. A VHR mode experiment was also conducted to observe the ultimate resolution capability of the Dichotom-I system, and a resolution of 4.2 mm FWHM was obtained at the expense of sensitivity which was reduced by a factor of four from the HR mode experiment. The experience gained with Dichotom-I suggests a relatively simple and inexpensive modification of the existing NaI(T1) ring positron cameras, most of which suffer from low resolution due to poor sampling and poor intrinsic detector resolution.