Positive streamers in air and other oxygen-nitrogen mixtures are generally believed to propagate against the electron drift direction due to photo-ionization. Photo-ionization is the non-local ionization of O2-molecules by UV radiation from excited N2-molecules. This facilitates the streamer propagation by creating free electrons ahead of it. The relative importance of photo-ionization depends on the O2/N2 ratio. Another possible source of free electrons in front of the positive streamer is background ionization. This can be ionization left by previous discharges or by other processes such as cosmic rays or (natural) radio-activity. We study the effects of both photo- and background-ionization on propagation and morphology of positive strea...