Selective Laser Melting (SLM) was used to fabricate scaffolds using the titanium alloy Ti-6Al-4V. Two types of high porosity open-cell structures were manufactured: the first built from topology optimised designs with maximised stiffness, and the second from gyroid labyrinths. In mechanical compression tests the scaffolds demonstrate exceptional strength- and stiffness-to-weight ratios. In particular, for densities in the range 0.2-0.8g/cm3 the topology optimised scaffolds have specific strength and stiffness that are superior to those of comparable materials in the literature. In addition, the optimised scaffolds have the benefit of being elastically isotropic. The results of finite element calculations accurately match the measured stiffness of the scaffolds. Calculated strain energy distributions provide insight into how the high stiffness and strength of the optimised designs is connected to their efficient distribution of load.