Distributed databases operating over wide-area networks, such as the Internet, must deal with the unpredictable nature of the performance of communication. The response times of accessing remote sources may vary widely due to network congestion, link failure, and other problems. In this paper we examine a new class of methods, called query scrambling, for dealing with unpredictable response times. Query scrambling dynamically modifies query execution plans on-the-fly in reaction to unexpected delays in data access. We explore various choices in the implementation of these methods and examine, through a detailed simulation, the effects of these choices. Our experimental environment considers pipelined and non-pipelined join processing in a client with multiple remote data sources and it focuses on bursty arrivals of data. We identify and study a number of the basic trade-offs that arise when designing scrambling policies for the bursty environment. Our performance results show that query scrambling is effective in hiding the impact of delays on query response time for a number of different delay scenarios. (Also cross-referenced as UMIACS-TR-96-84)