Searches are reported for Higgs bosons in the context of either the standard model extended to include a fourth generation of fermions (SM4) with masses of up to 600 GeV or fermiophobic models. For the former, results from three decay modes (tau tau, WW, and ZZ) are combined, whilst for the latter the diphoton decay is exploited. The analysed proton-proton collision data correspond to integrated luminosities of up to 5.1 inverse femtobarns at 7 TeV and up to 5.3 inverse femtobarns at 8 TeV. The observed results exclude the SM4 Higgs boson in the mass range 110-600 GeV at 99% confidence level (CL), and in the mass range 110-560 GeV at 99.9% CL. A fermiophobic Higgs boson is excluded in the mass range 110-147 GeV at 95% CL, and in the range 110-133 GeV at 99% CL. The recently observed boson with a mass near 125 GeV is not consistent with either an SM4 or a fermiophobic Higgs boson.