The FAST satellite has detected a class of ion conic events in which He+ is more strongly accelerated than H+ or O+. The helium ions in these events typically have 3–30 times the energy of simultaneously observed protons, unlike most conics, in which no strong preferential acceleration occurs. These events are well correlated with the occurrence of electromagnetic ion cyclotron (EMIC) waves and are associated with inverted-V electron distributions. The acceleration mechanism is similar to a mechanism which has been proposed for the acceleration and enrichment of 3He in impulsive solar flares. We present a statistical study of such events in the FAST data set. We show that these events are found primarily in the pre-midnight sector and that their occurrence distribution is similar to the distributions previously found for inverted-V electron events and for EMIC waves.