Space-based Global Navigation Satellite System Reflectometry (GNSS-R) altimetry remains an open challenge. This paper reports on space-based GNSS-R altimetry using 40-s period of intermediate frequency recording from the TechDemoSat-1 mission. This recording is unique because one GPS signal is reflected from ice. The waveforms that are used to determine path delay are generated by 1 ms coherent integration. Pseudoranges are smoothed every 0.5 s by linear models before calculating the path delay. Altimetric results are compared to DTU10 mean sea surface heights, with good agreement being obtained. The RMS difference of 4.4 m is much smaller than reported in the current literature. Very good altimetric precision of better than 1 m (0.96 m) is achieved with a spatial resolution of 3.8 km. This result validates the potential of space-based GNSS-R altimetry.