In opportunistic Cognitive Radio Networks (CRNs), which are characterized by changing network topology, the time and location varying spectrum availability, there is a need of on-demand searching for a control traffic channel by cognitive radio (CR) users in order to be able to initiate a communication. Therefore, the neighborhood discovery phase, also referred to as a rendezvous (RDV) phase, is challenging due to the dynamics of such networks. Lately, there has been a proliferation of different rendezvous protocols. However, mostly the proposed protocols have had a narrow focus, which is usually a RDV guarantee in a single cycle. At times there is support for a RDV guarantee on every unoccupied channel in a single cycle, however, very rarely asynchronism is exploited as a main factor, or considering channel heterogeneity in terms of quality.In this study we show how to add and benefit from asynchronism in neighborhood discovery protocols that already guarantee a RDV on each free channel. Thanks to induced asynchronism, the ranking of channels is introduced, allowing nodes to stay longer on better quality channels. We analyze the behavior of three different rendezvous protocols in terms of efficiency and time-to-rendezvous with the measured error margins for different asynchronous offsets. We show that an asynchronism significantly improves the efficiency of all the studied protocols. The goal of this paper Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. MobiWacis not to proof that one particular protocol is better than another, we aim only to show that the added asynchronism and induced ranking of channels can improve significantly the performance of different rendezvous protocols.