Low-density nanocellular polymers are required to take advantage of the full potential of these materials as high efficient thermal insulators. However, their production is still a challenging task. One promising approach is the use of nanostructured polymer blends of poly(methyl methacrylate) (PMMA) and a block copolymer poly(methyl methacrylate)-poly(butyl acrylate)-poly(methyl methacrylate) (MAM), which are useful for promoting nucleation but seem to present a severe drawback, as apparently avoid low relative densities. In this work, new strategies to overcome this limitation and produce low-density nanocellular materials based on these blends are investigated. First, the effect of very low amounts of the MAM copolymer is analysed. It is detected that nanostructuration can be prevented using low copolymer contents, but nucleation is still enhanced as a result of the copolymer molecules with high CO2 affinity dispersed in the matrix, so nanocellular polymers are obtained using very low percentages of the copolymer. Second, the influence of the foaming temperature is studied. Results show that for systems in which there is not a clear nanostructuration, cells can grow more freely and smaller relative densities can be achieved. For these studies, blends of PMMA with MAM with copolymer contents from 10 wt% and as low as 0.1 wt% are used. For the first time, the production strategies proposed in this work have allowed obtaining low density (relative density 0.23) nanocellular polymers based on PMMA/MAM blends.