Consider an infinite iterated function system on the line, with polynomially decreasing size of cylinders. The problem I'm going to consider is: how big is the set of points whose symbolic expansion grows at least with some prescribed speed. Surprisingly, while the packing dimension of such set depends only on the growth condition and the rate of decrease of sizes of cylinders, for Hausdorff dimension the placement of maps (order, presence of gaps) matters as well.