Satellite nadir radar altimeters have been widely used to measure river and lake surface water elevations. They can now retrieve the elevations of some rivers <200 m wide. However, as these satellite missions are primarily designed to observe ocean surface topography, they are not always able to observe continental surfaces. For steep-sided rivers (i.e. in river valleys no more than a few km wide and surrounded by slopes over 50 m high), altimeters tend to observe the top of the surrounding topography rather than the river itself. The Jason-3 altimetry mission, launched in January 2016, has an alternative instrument operation mode, the so called Open-Loop (OL) or Digital Elevation Model (DEM) tracking mode. This mode is intended to help overcome this issue, by using an on-board DEM. However it was not used in 2016 as the operational mode because of difficulties in defining an accurate on-board global-scale DEM. Mainland France has been chosen to test the OL tracking mode, as water masks and DEMs of sufficient accuracy are available. Following the launch of Jason-3, Jason-2 (its predecessor) was maintained on the same nominal orbit as its follow-on, for more than 6 months. During this tandem period, data from the first 10 Jason-3 cycles (a Jason-2/-3 cycle corresponds to 10 days) were acquired in the traditional Closed-Loop (CL) tracking mode. Jason-3 data from the last 13 cycles were acquired in OL tracking mode. Jason-2 was always in CL tracking mode. Compared to nearby in situ gages and for river wider than 100 m, Jason-3 water elevation anomalies have a RMSE between 0.20 and 0.30 m for most reaches. Jason-3 performance over narrow rivers is similar to that of Jason-2. In CL tracking mode, Jason-3 altimeter tends to be locked over the surrounding topography more frequently than Jason-2 (due to the specific post-launch Jason-2 altimeter tuning). This study shows that Jason-2 observed 60% of river reaches studied (48 of 86 reaches), whereas Jason-3 in OL tracking mode was able to measure all river reaches for every cycle. This result clearly highlights the significant advantages of the OL tracking mode for observation of steep-sided rivers. However, further investigations are required to compute an accurate on-board global-scale DEM and to determine those locations where the use of OL tracking mode is or is not appropriate.