Case studies show that some energetic particle flux enhancements up to MeV/nuc. observed at 1 AU cannot be treated as a consequence of particle acceleration at shocks or during flares. Atypical energetic particle events (AEPEs) are often detected during crossings of magnetic cavities formed by strong current sheets of various origins in the solar wind. Such cavities confine small-scale magnetic islands (SMIs) produced by magnetic reconnection. SMIs, in turn, trap and re-accelerate energetic particles according to predictions based on the theory of Zank et al. describing stochastic particle energization in the supersonic solar wind via numerous dynamically interacting SMIs. AEPEs possess energies that overlap SEP events and can be an important component in understanding space weather.