In electronic cooling with superconducting tunnel junctions, the cooling power is counterbalanced by the interaction with phonons and by the heat flow from the overheated leads. We study aluminum-based coolers that are equipped with a suspended normal metal and an efficient quasiparticle drain. At intermediate temperatures, the phonon bath of the suspended normal metal is cooled. By adjusting the junction transparency, we control the injection current and, thus, the temperature of the superconducting lead at the optimum cooling point. The best device shows remarkable cooling from 150 mK down to about 30 mK, a factor of 5 in temperature at a power of 40 pW. We discuss heat transport in our device and the reasons for cooling saturation at the low-temperature end.