It was suggested that multilayered accretionary rims composed of ferrous olivine, andradite, wollastonite, salite-hedenbergitic pyroxenes, nepheline, and Ni-rich sulfides around Allende calcium aluminum-rich inclusions (CAIs) are aggregates of gas-solid condensates which reflect significant fluctuations in physico-chemical conditions in the slowly cooling solar nebula and grain/gas separation processes. In order to test this model, we studied the mineralogy of accretionary rims around one type A CAI (E104) and one type B CAI (E48) from the reduced CV3 chondrite Efremovka, which is less altered than Allende. In contrast to the Allende accretionary rims, those in Efremovka consist of coarse-grained (20-40 mum), anhedral forsterite (Fa(1-8)), Fe,Ni-metal nodules, amoeboid olivine aggregates (AOAs) and fine-grained CAIs composed of Al-diopside, anorthite, and spinel, +/- forsterite. Although the fine-grained CAIs, AOAs and host CAIs are virtually unaltered, a hibonite-spinel-perovskite CAI in the E48 accretionary rim experienced extensive alteration, which resulted in the formation of Fe-rich, Zn-bearing spinel, and a Ca, Al, Si-hydrous mineral. Forsterites in the accretionary rims typically show an aggregational nature and consist of small olivine grains with numerous pores and tiny inclusions of Al-rich minerals. No evidence for the replacement of forsterite by enstatite was found; no chondrule fragments were identified in the accretionary rims.