A search is performed for production of short-lived particles in e + e − → XY, with X → γγ and Y → ff, for scalar X and scalar or vector Y. Model-independent limits in the range of 25-60 femtobarns are presented on σ(e + e − → XY) × B(X → γγ) × B(Y → ff) for centre-of-mass energies in the range 205−207 GeV. The data from all LEP centre-of-mass energies 88−209 GeV are also interpreted in the context of fermiophobic Higgs boson models, for which a lower mass limit of 105.5 GeV is obtained for a "benchmark" fermiophobic Higgs boson.