This paper presents several case studies which illustrate how constraint programming can benefit from the combination of global and local search techniques, offering a flexible and efficient platform for the design of combinatorial optimisation applications. For job-shop scheduling, we relate experiments with local search procedures that use global search to intensively explore a given neighbourhood, in the spirit of “shuffle” methods. For preemptive job-shop scheduling, two basic search strategies, Depth-First Search and Limited Discrepancy Search, are compared. For Vehicle Routing we report an Incremental Local Optimisation heuristic, combined with Limited Discrepancy Search. Finally, we show how ad hoc algebras can considerably enhance the design of heuristics based on local and global search within a constraint-programming environment. Experiments on vehicle routing will enlighten how such a language for “search and insert” control can enable automated tuning and discovery of new strategies adapted to the instances typology of the problem at stake.