Practical and efficient algorithms for concurrent data structures are difficult to construct and modify. Algorithms in the literature are often optimized for a specific setting, making it hard to separate the algorithmic insights from implementation details. The goal of this work is to systematically construct algorithms for a concurrent data structure starting from its sequential implementation. Towards that goal, we follow a construction process that combines manual steps corresponding to high-level insights with automatic exploration of implementation details. To assist us in this process, we built a new tool called Paraglider. The tool quickly explores large spaces of algorithms and uses bounded model checking to check linearizability of algorithms. Starting from a sequential implementation and assisted by the tool, we present the steps that we used to derive various highly-concurrent algorithms. Among these algorithms is a new fine-grained set data structure that provides a wait-free contains operation, and uses only the compare-and-swap (CAS) primitive for synchronization.