Constraint combination methods are essential for a flexible constraint programming system. This paper presents deep concurrent constraint combinators based on computation spaces as combination mechanism. It introduces primitives and techniques needed to program constraint combinators from computation spaces. The paper applies computation spaces to a broad range of combinators: negation, generalized reification, disjunction, and implication. Even though computation spaces have been conceived in the context of Oz, they are mainly programming language independent. This point is stressed by discussing them here in the context of Standard ML with concurrency features.