Density-functional theory (DFT) has become an extensively and successfully used tool in the studies of molecules and materials. However, DFT remains computationally expensive, especially for exploring the conformational space of molecular systems comprising a few hundred atoms. Here, we present a Reduced Approach to Density-functional Expansion (RADE), devised to substantially reduce the computational cost of standard DFT methods. RADE can be implemented fully non-empirically as an efficient first-principles electronic structure method. Preliminary results for molecules containing elements H, C, N, and O indicate that this method can, in general, reproduce well the results from standard DFT calculations.