Pollination by sexual deception is arguably one of the most unusual liaisons linking plants and insects, and perhaps the most illustrative example of extreme floral specialization in angiosperms. While considerable progress has been made in understanding the floral traits involved in sexual deception, less is known about how this remarkable mimicry system might have arisen, the role of pre-adaptations in promoting its evolution and its extent as a pollination mechanism outside the few groups of plants (primarily orchids) where it has been described to date. In the Euro-Mediterranean region, pollination by sexual deception is traditionally considered to be the hallmark of the orchid genus Ophrys. Here, we introduce two new cases outside of Ophrys, in plant groups dominated by generalized, shelter-mimicking species. On the basis of phylogenetic reconstructions of ancestral pollination strategies, we provide evidence for independent and bidirectional evolutionary transitions between generalized (shelter mimicry) and specialized (sexual deception) pollination strategies in three groups of flowering plants, and suggest that pseudocopulation has evolved from pre-adaptations (floral colours, shapes and odour bouquets) that selectively attract male pollinators through shelter mimicry. These findings, along with comparative analyses of floral traits (colours and scents), shed light on particular phenotypic changes that might have fuelled the parallel evolution of these extraordinary pollination strategies. Collectively, our results provide the first substantive insights into how pollination sexual deception might have evolved in the Euro-Mediterranean region, and demonstrate that even the most extreme cases of pollinator specialization can reverse to more generalized interactions, breaking 'Cope's rule of specialization'.