Due to the OPTIONAL operator, the core fragment of the SPARQL query language is non-monotonic. That is, some solutions of a query result can be returned to the user only after having consulted all relevant parts of the queried dataset(s). This property presents an obstacle when developing query execution approaches that aim to reduce responses times rather than the overall query execution times. Reducing the response times?i.e., returning as many solutions as early as possible? is important in particular in Web-based client-server query processing scenarios in which network latencies dominate query execution times. Such scenarios are typical in the context of integration of Web data sources where a data integration component executes queries over a decentralized federation of such data sources. In this paper we introduce an alternative operator that is similar in spirit to OPTIONAL but without causing non-monotonicity. We show fundamental properties of this operator and observe that the downside of achieving the desired monotonicity property is a potentially significant increase in query result sizes. We study the extend of this trade-off in practice.