The proposal herein is based on an efficient sulfur host, namely hierarchical microporous-mesoporous carbonaceous nanotubes (denoted as HMMCNT) that feature a thick microporous wall and inner hollow channel. The electrochemical performance of the composite (HMMCNT-S) is studied systematically at different discharge cut-off voltages and at varying sulfur content. The cycling behavior in different voltage windows is compared and the highest specific capacity is shown for HMMCNT-S-50 in the range of 1.4-2.8 V. These results imply that better energy densities can be achieved by controlling the discharge cut-off voltage. Moreover, we show that when the sulfur loading is 50% (HMMCNT-S-50), the cycling and rate performance is better than that of the composite loaded with 40% sulfur (HMMCNT-S-40). Benefiting from the attractive hierarchical micro/mesoporous configuration, the obtained hybrid structure not only promotes electron and ion transfer during the charge/discharge process, but also efficiently impedes polysulfide dissolution. More specifically, the electrode can deliver a specific capacity of 558 mA h g(-1) even after 150 cycles at a high rate of 1600 mA g(-1) with a decay rate of only 0.13% per cycle. Considering the beneficial structure of these carbon nanotubes, it is very feasible that these structures may also be used in other research fields, including in catalysis, as supercapacitors, in drug-delivery applications, for absorption, and so on.