Abstract
We study new classes of overpartitions of numbers based on the properties of nonoverlined parts. Several combinatorial iden-tities are established by means of generating functions and bijective proofs. We show that our enumeration function satisfies a pair of infi-nite Ramanujan-type congruences modulo 3. Lastly, by conditioning on the overlined parts of overpartitions, we give a seemingly new identity between the number of overpartitions and a certain class of ordinary partition functions. A bijective proof for this theorem also includes a partial answer to a previous request for a bijection on partitions doubly restricted by divisibility and frequency.