The improved variant of the local correlation coupled-cluster (CC) framework termed "cluster-in-molecule" (CIM), defining the single-environment (SE) CIM-CC approach, is presented and tested at the CC singles and doubles (CCSD) level. In the proposed SECIM-CC method, the previous design of the CIM orbital subsystems [Li, W.; Gour, J. R.; Piecuch, P.; Li, S. J. Chem. Phys. 2009, 131, 114109], referred to as the dual-environment (DE) CIM-CC approach, which is based on the ideas of central orbitals and the associated primary and secondary environments, is replaced by the simplified design in which the central localized molecular orbitals (LMOs) and the corresponding environment LMOs are first assigned to each nonhydrogen atom and the hydrogen atoms that are bound to it. The SECIM-CC approach offers improvements in the DECIM-CC results, particularly for weakly bound molecular clusters using diffuse basis functions. Through the use of a single parameter to define the environment LMOs and through the assignment of subsystem LMOs to atoms, the SECIM-CC calculations are easy to control and the CIM subsystems do not unnecessarily vary with the nuclear geometry, creating smoother potential energy surfaces. The performance of SECIM-CCSD is illustrated by the calculations for normal alkanes and water clusters described by the 6-31G(d), 6-31++G(d,p), and 6-311++G(d,p) basis sets.