Skylines with partial order preference semantics often result in huge answer sets and what is worse, they cannot be computed efficiently. In this paper we will explore the evaluation of so-called restricted skyline queries with partial order preferences under the paradigm of weak Pareto dominance. Weak Pareto dominance removes all objects from skylines, which are dominated by other objects in some query predicates, but in turn do not dominate these objects in any predicate. We will argue that this paradigm yields intuitive results, prove that it leads to lean sizes of the restricted skyline and show how it opens up the use of efficient algorithms for evaluation adopting the iteration of ranked result lists for each query predicate.