Atwisted stack of high-temperature superconducting (HTS) tapes soldered into copper profiles was used as a strand in the fabrication of the 60-kA/ 12-T HTS cable prototype at the Center for Research in Plasma Physics (CRPP). Considering the strand in general as a modular element for the high-current cables, design parameters of the strand need to be optimized in order to best fulfill requirements of appropriate application field. During the development program of the HTS fusion cable at CRPP, influence of the design parameters on the strand's performance was obtained as input data for the optimization process. In this paper, we summarize the results of the twisting, bending, and transverse pressure tests on strands of various tapes and profile's geometries. Finite-element model for the transverse pressure test was developed, validated with the test results, and used for the design proposals. Effect of the stack aspect ratio, tape properties, and anisotropy, as well as selection of HTS material for the strand, will be discussed.