First-principles calculations are performed to investigate energetic and atomistic characteristics of ferroelectric domains walls (DWs) of BiFeO(3) (BFO) films subject to compressive strain. Significantly lower DW energies than those previously reported, and a different energetic hierarchy between the various DW types, are found for small strains. In all investigated cases (corresponding to ideal angles of 71°, 109°, and 180° formed by the domain polarizations), the DW energy reaches its maximum value for misfit strains that are around the critical strain at which the transition between the R-like and T-like phases occurs in single-domain BFO. Near these strains, several quantities depend strongly on the type of domain wall; such distinct behavior is associated with an elastic difference and a large out-of-plane polarization at the DW in the 180° case. A further increase of the magnitude of the strain leads to (i) a change of hierarchy of the DW energies, (ii) large out-of-plane polarizations inside each up and down domain, and (iii) novel atomic arrangements at the domain walls. Our study can thus initiate a new research direction, namely strain engineering of domain-wall functionalities.