  Positive streamer discharges have been studied and modelled extensively in
air. Here we study positive streamers in CO$_2$ with and without oxygen
admixtures; they are relevant for current high voltage technology as well as
for discharges in the atmosphere of Venus. We discuss that no efficient
photoionization mechanism is known for gases with a large CO$_2$ fraction, as
photons in the relevant energy range are rapidly absorbed. Hence positive
streamers can propagate only due to some other source of free electrons ahead
of the ionization front. Therefore we study positive streamer propagation in
CO$_2$ with different levels of background ionization to provide these free
electrons. The effect of replacing photoionization by background ionization is
studied with simulations in air. Simulating streamers in background fields of
16 to 20~kV/cm at standard temperature and pressure within a gap of 6.4~cm, we
find that streamer propagation is rather insensitive to the level of
photoionization or background ionization. We also discuss that the results
depend not only on the value of breakdown field and applied electric field, and
on preionization or photoionization, but also on the electron mobility $\mu(E)$
and the effective ionization coefficient $\alpha_{\rm eff}(E)$, that are
gas-dependent functions of the electron energy or the electric field.
