Due to their appealing properties such as high-temperature dimensional stability, chemical resistance, compressive strength and recyclability, new-generation foams based on engineering thermoplastics such as polyethylene terephthalate (PET) and polybutylene terephthalate (PBT) have been gaining significant attention. Achieving low-density foams without sacrificing the mechanical properties is of vital importance for applications in the field of transportation and construction, where sufficient compressive strength is desired. In contrast to numerous research studies on PET foams, only a limited number of studies on PBT foams and in particular, on extruded PBT foams are known. Here we present a novel route to extruded PBT foams with densities as low as 80 kg/m3 and simultaneously with improved compressive properties manufactured by a tandem reactive-extrusion process. Improved rheological properties and therefore process stability were achieved using two selected 1,3,5-benzene-trisamides (BTA1 and BTA2), which are able to form supramolecular nanofibers in the PBT melt upon cooling. With only 0.08 wt % of BTA1 and 0.02 wt % of BTA2 the normalized compressive strength was increased by 28% and 15%, respectively. This improvement is assigned to the intrinsic reinforcing effect of BTA fibers in the cell walls and struts.