A new approximation strategy, split-amplitude strategy, useful within the framework of the coupled-cluster (CC). methodology is proposed. It consists in representing the individual cluster amplitudes as a sum of two components, one of fixed value, which may be obtained from external sources, and the other determined from a set of modified CC equations. This approach provides new possibilities of absorbing information concerning the values of cluster amplitudes from independent calculations. By properly choosing the fixed amplitude components, one may substantially reduce the magnitudes of the most significant amplitudes to be determined for the state considered, which in turn causes that the known approximation procedures are more justifiable when applied to the modified CC equations than to the equations of the standard CC approaches. The split-amplitude strategy has been employed to setting up several almost-linear CC (AL-CC) approaches of a single reference type corresponding to the basic CC methods. These low-cost approaches seem to be useful. in theories of processes involving nondynamically correlated (quasidegenerate) states. The AL-CC methods have been applied to the ground states for various geometries of the following molecular systems : H8, H2O, BH, and HF. It is found that the energies obtained for a given AL-CC approach are very close to those for the corresponding basic CC method, which is,true even for strongly quasidegenerate states.