Most 2.5D controlled-source electromagnetic (CSEM) modeling algorithms presented to date explicitly consider only sources that are point dipoles oriented parallel or perpendicular to the direction of constant conductivity. This makes simulations of complex source geometries expensive, requiring separate evaluations of many point dipole fields, and thus limits the practical applicability of such schemes for simulating and interpreting field data. We present a novel 2.5D CSEM modeling scheme that overcomes this limitation and permits efficient simulations of sources with general shape and orientation by evaluating fields for the entire source at once. We accommodate general sources by using a secondary field approach, in which primary fields are computed for the general source and a 1D background conductivity model. To carry out the required Fourier transforms between space and wavenumber domain using the same fast cosine and sine transform filters as in conventional algorithms, we split the primary and secondary fields into their symmetric and antisymmetric parts. For complex 3D source geometries, this approach is significantly more efficient than previous 2.5D algorithms. Our finite-difference algorithm also includes novel approaches for divergence correction at low frequencies and EM field interpolation across conductivity discontinuities. We describe the modeling scheme and demonstrate its accuracy and efficiency by comparisons of 2.5D-simulated data with 1D and 3D results.