Accessing numerous widely-distributed data sources poses significant new challenges for query optimization and execution. Congestion or failure in the network introduce highly-variable response times for wide-area data access. This paper is an initial exploration of solutions to this variability. We investigate a class of dynamic, run-time query plan modification techniques that we call query plan scrambling. We present an algorithm which modifies execution plans on-the-fly in response to unexpected delays in data access. The algorithm both reschedules operators and introduces new operators into the plan. We present simulation results that show how our technique effectively hides delays in receiving the initial requested tuples from remote data sources. (Also cross-referenced as UMIACS-TR-96-35)