  We report the discovery of two exoplanets around the M dwarfs GJ 724 and GJ
3988 using the radial velocity (RV) method. We obtained a total of 153 3.5 m
Calar Alto/CARMENES spectra for both targets and measured their RVs and
activity indicators. We also added archival ESO/HARPS data for GJ 724 and
infrared RV measurements from Subaru/IRD for GJ 3988. We searched for periodic
and stable signals to subsequently construct Keplerian models, considering
different numbers of planets, and we selected the best models based on their
Bayesian evidence. Gaussian process (GP) regression was included in some models
to account for activity signals. For both systems, the best model corresponds
to one single planet. The minimum masses are $10.75^{+0.96}_{-0.87}$ and
$3.69^{+0.42}_{-0.41}$ Earth-masses for GJ 724 b and GJ 3988 b, respectively.
Both planets have short periods (P < 10 d) and, therefore, they orbit their
star closely (a < 0.05 au). GJ 724 b has an eccentric orbit (e =
$0.577^{+0.055}_{-0.052}$), whereas the orbit of GJ 3988 b is circular. The
high eccentricity of GJ 724 b makes it the most eccentric single exoplanet (to
this date) around an M dwarf. Thus, we suggest a further analysis to understand
its configuration in the context of planetary formation and architecture. In
contrast, GJ 3988 b is an example of a common type of planet around mid-M
dwarfs.
