We investigate a set of donor-pi-acceptor (D-pi-A) dyes with new acceptor groups for dye-sensitized solar cells, using time-dependent density-functional-theory calculations of the electronic structure and optical absorption. We considered three types of modifications on existing dye structures: (i) replacement of the side cyano group (CN) on the molecular anchor, (ii) insertion and alteration of the intermediate spacer groups, and (iii) modification of the number and positions of cyano CN groups on a phenyl-ring spacer. We find that with these modifications, the dye electronic levels and corresponding optical absorption properties can be gradually tuned, rendering possible the identification of dyes with desirable structural, electronic, and optical properties. For example, dyes with phenyl and CN-substituted phenyl groups are promising candidates for red light absorption and high molar extinction coefficients.