The mechanical responses of syntactic foams comprising hollow thermoplastic micro-spheres (HTMs) embedded in a polyurethane matrix were experimentally examined under uniaxial compressive strain. Phenomenological strain energy models were subsequently developed which capture both the axial stress-strain and transverse strain response of the foams. HTM syntactic foams were found to exhibit increased small-strain stiffness with reduced density, revealing a highly-tuneable and extremely lightweight syntactic foam blend for mechanical applications. The foams were also found to possess strong compressibility ($J \approx 0.75$) and a high threshold for plastic deformation, making them a robust alternative to hollow glass microsphere (HGM) syntactic foams. The non-standard transverse strain relationship exhibited by HTM syntactic foams at high filling fractions was captured by advanced strain energy models.