  Context: The main goal of the CARMENES survey is to find Earth-mass planets
around nearby M-dwarf stars. Seven M-dwarfs included in the CARMENES sample had
been observed before with HIRES and HARPS and either were reported to have one
short period planetary companion (GJ15A, GJ176, GJ436, GJ536 and GJ1148) or are
multiple planetary systems (GJ581 and GJ876).
  Aims: We aim to report new precise optical radial velocity measurements for
these planet hosts and test the overall capabilities of CARMENES.
  Methods: We combined our CARMENES precise Doppler measurements with those
available from HIRES and HARPS and derived new orbital parameters for the
systems. Bona-fide single planet systems are fitted with a Keplerian model. The
multiple planet systems were analyzed using a self-consistent dynamical model
and their best fit orbits were tested for long-term stability.
  Results: We confirm or provide supportive arguments for planets around all
the investigated stars except for GJ15A, for which we find that the
post-discovery HIRES data and our CARMENES data do not show a signal at 11.4
days. Although we cannot confirm the super-Earth planet GJ15Ab, we show
evidence for a possible long-period ($P_{\rm c}$ = 7025$_{-629}^{+972}$ d)
Saturn-mass ($m_{\rm c} \sin i$ = 51.8$_{-5.8}^{+5.5}M_\oplus$) planet around
GJ15A. In addition, based on our CARMENES and HIRES data we discover a second
planet around GJ1148, for which we estimate a period $P_{\rm c}$ =
532.6$_{-2.5}^{+4.1}$ d, eccentricity $e_{\rm c}$ = 0.34$_{-0.06}^{+0.05}$ and
minimum mass $m_{\rm c} \sin i$ = 68.1$_{-2.2}^{+4.9}M_\oplus$.
  Conclusions: The CARMENES optical radial velocities have similar precision
and overall scatter when compared to the Doppler measurements conducted with
HARPS and HIRES. We conclude that CARMENES is an instrument that is up to the
challenge of discovering rocky planets around low-mass stars.
