We define a new class of low-communication voting rules, tailored for contexts with few voters and possibly many candidates. These rules are defined by a predefined sequence of voters: at each stage, the designated voter eliminates a candidate, and the last remaining candidate wins. We study deterministic and randomized versions of these rules. We first investigate their axiomatic properties. Then we focus on a subfamily of rules defined by "non-interleaved" sequences, for which we seek a sequence that best approximates the Borda rule under Impartial Culture. Finally, we apply our rules to randomly generated data.