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In orthogonal frequency division multiple access networks, link adaptation (LA) selects the appropriate modulation and coding scheme for the upcoming transmission time interval. Since LA relies on measurements of the interference level and assumes that it remains similar during the next scheduling instance, the performance of LA depends on the variation (rather than simply the level) of intercell interference (ICI). In this paper we propose a minimum variance scheduler that allows for opportunistic scheduling - and thereby to take advantage of multi-user frequency diversity - but keeps the variation of intercell interference at a low level. We build on previously proposed collision models (detailed in own work and related other papers) and study the interplay between this scheduler and two intercell interference coordination (ICIC) methods that we call random and coordinated subcarrier allocation. We find that the proposed low variance scheduling scheme together with coordinated ICIC reduces ICI and its variance and is superior to other scheduling techniques in terms of the overall system throughput.