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In dataflow analysis of logic programs, information must be propagated according to the control strategy of the language under consideration. However, for languages with top-down control flow, naive top-down dataflow analyses may have problems guaranteeing completeness and/or termination. What is required in the dataflow analysis is a bottom-up fixpoint computation, guided by the (possibly top-down) control strategy of the language. This paper describes the application of the Magic Templates algorithm, originally devised as a technique for efficient bottom-up computation of logic programs, to dataflow analysis of logic programs. It turns out that a direct application of the Magic Templates algorithm can result in an undesirable loss in precision, because connections between ``calling patterns'' and the corresponding ``success patterns'' may be lost. We show how the original Magic Templates algorithm can be modified to avoid this problem, and prove that the resulting analysis algorithm is at least as precise as any other abstract interpretation that uses the same abstract domain and abstract operations.