Although M dwarfs are known for high levels of stellar activity , they are ideal targets for the search of low-mass exoplanets with the radial velocity method . We report the discovery of a planetary-mass companion around LSPM J2116+0234 ( M3.0 V ) and confirm the existence of a planet orbiting GJ 686 ( BD+18 3421 ; M1.0 V ) . The discovery of the planet around LSPM J2116+0234 is based on CARMENES radial velocity observations in the visual and near-infrared channels . We confirm the planet orbiting around GJ 686 by analyzing the radial velocity data spanning over two decades of observations from CARMENES VIS , HARPS-N , HARPS , and HIRES . We find planetary signals at 14.44 and 15.53 d in the radial velocity data for LSPM J2116+0234 and GJ 686 , respectively . Additionally , the radial velocity , and photometric time series , as well as various spectroscopic indicators , show hints of variations of 42 d for LSPM J2116+0234 and 37 d for GJ 686 , which we attribute to the stellar rotation periods . The orbital parameters of the planets are modeled with Keplerian fits together with correlated noise from the stellar activity . A mini-Neptune with a minimum mass of 11.8 M _ { \oplus } orbits LSPM J2116+0234 producing a radial velocity semi-amplitude of 6.19 m s ^ { -1 } , while a super-Earth of mass 6.6 M _ { \oplus } orbits GJ 686 and produces a radial velocity semi-amplitude of 3.0 m s ^ { -1 } . Both LSPM J2116+0234 and GJ 686 have planetary companions populating the regime of exoplanets with masses lower than 15 M _ { \oplus } and orbital periods ยก20 d .