Fuzzing has proven to be a fundamental technique to automated software testing but also a costly one. With the increased adoption of CI/CD practices in software development, a natural question to ask is `What are the best ways to integrate fuzzing into CI/CD pipelines considering the velocity in code changes and the automated delivery/deployment practices?'. Indeed, a recent study by Böhme and Zhu shows that four in every five bugs have been introduced by recent code changes (i.e. regressions). In this paper, we take a close look at the integration of fuzzers to CI/CD pipelines from both automated software testing and continuous development angles. Firstly, we study an optimization opportunity to triage commits that do not require fuzzing and find, through experimental analysis, that the average fuzzing effort in CI/CD can be reduced by ~63% in three of the nine libraries we analyzed (>40% for six libraries). Secondly, we investigate the impact of fuzzing campaign duration on the CI/CD process: A shorter fuzzing campaign such as 15 minutes (as opposed to the wisdom of 24 hours in the field) facilitates a faster pipeline and can still uncover important bugs, but may also reduce its capability to detect sophisticated bugs. Lastly, we discuss a prioritization strategy that automatically assigns resources to fuzzing campaigns based on a set of predefined priority strategies. Our findings suggest that continuous fuzzing (as part of the automated testing in CI/CD) is indeed beneficial and there are many optimization opportunities to improve the effectiveness and scalability of fuzz testing.