Providing efficient emulations of atomic read/write objects in asynchronous, crash-prone, message-passing systems is an important problem in distributed computing. Communication latency is a factor that typically dominates the performance of message-passing systems, consequently the efficiency of algorithms implementing atomic objects is measured in terms of the number of communication exchanges involved in each read and write operation. The seminal result of Attiya, Bar-Noy, and Dolev established that two pairs of communication exchanges, or equivalently two round-trip communications, are sufficient. Subsequent research examined the possibility of implementations that involve less than four exchanges. The work of Dutta et al. showed that for single-writer/multiple-reader (SWMR) settings two exchanges are sufficient, provided that the number of readers is severely constrained with respect to the number of object replicas in the system and the number of replica failures, and also showed that no two exchange implementations of multiple-writer/multiple-reader (MWMR) objects are possible. Later research focused on providing implementations that remove the constraint on the number of readers, while having read and write operations that use variable number of communication exchanges, specifically two, three, or four exchanges. This work presents two advances in the state-of-the-art in this area. Specifically, for SWMR and MWMR systems algorithms are given in which read operations take two or three exchanges. This improves on prior works where read operations took either (a) three exchanges, or (b) two or four exchanges. The number of readers in the new algorithms is unconstrained, and write operations take the same number of exchanges as in prior work (two for SWMR and four for MWMR settings). The correctness of algorithms is rigorously argued.