A family of modified GAUSSIAN-2 (G2M) calculational schemes have been proposed, based on geometry optimization and vibrational frequency calculations using the hybrid density-functional approach, and electron correlation evaluation using the coupled-cluster methods. The most accurate model, called G2M(RCC), gives the average absolute deviation of calculated atomization energies from experiment for 32 first-row compounds of 0.88 kcal/mol. The other two methods, called G2M(RCC,MP2) and G2M(rcc,MP2), exhibit the average absolute deviations of 1.15 and 1.28 kcal/mol, respectively, and can be used for the calculations of molecules and radicals of larger sizes containing up to six to seven heavy atoms. The G2M(rcc,MP2) model demonstrates an accuracy comparable to that of G2(MP2) and requires less intensive computations than the latter. The preference of the G2M(RCC) methods over the original G2 is expected to be particularly significant for the open shell systems with large spin contamination.