© 2018, The Author(s). A major goal in volcanology is to be able to constrain the physical properties of a volcanic system using surface observations. The behaviour of a volcanic system following an eruption can provide powerful constraints on these properties and can provide valuable information for understanding future hazard. We use spatially and temporally dense observations of surface deformation following the 12 June 2011 eruption of Nabro (Eritrea) to place constraints on the mechanics of its subsurface volcanic system. Nabro was imaged 129 times by TerraSAR-X and COSMO-SkyMed satellites during a 15-month period following the eruption. We have produced a detailed time series of the line-of-sight (LOS) displacements at Nabro, finding that the volcano subsides during the entire observation period at a decaying rate. We found significant atmospheric artefacts remained in the data set after a standard spatio-temporal filter was applied. Applying an empirical correction using a linear phase-elevation relationship removed artefacts but also removed real topographically correlated deformation. Instead, we were able to correct each SAR acquisition using independent delay estimates derived from the ECMWF ERA-Interim (ERA-I) global atmospheric model. The corrected time series can be modelled with the deflation of a Mogi source at ∼ 6.4 ± 0.3 km depth. Modelling the time series using viscoelastic relaxation of a shell which surrounds a spherical magma chamber can explain the observed subsidence without a source of further volume loss if the magma is compressible. CO2outgassing is also a possible cause of continued subsidence. Contraction due to cooling and crystallisation, however, is probably minor. If any post-eruptive recharge of the magmatic system at Nabro is occurring, the rate of recharge must be slower than the post-eruptive relaxation processes. Combined with the lack of pre-eruptive inflation, we suggest that recharge of the magmatic system at Nabro either occurs at a rate that is slower than our detection limit, or it occurs episodically. This case study demonstrates the power of long, dense geodetic time series at volcanoes.[Figure not available: see fulltext.].