A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for J → J, J − 1 transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the J → J − 1 case (i.e. J ′′ = 1 → J ′ = 0) and J → J case (i.e. J ′′ = 1/2 → J ′ = 1/2). A one dimensional (1D) model is presented and a complete 3D simulation using rate equations confirm the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the C − 2 molecular anion as a typical example of the interplay between the two simple transitions J → J, J − 1. Laser cooling and magneto-optical trapping of atoms typically involves J → J + 1 closed transitions driven by counter-propagating circularly polarized laser fields (J is the total angular momentum). On the contrary laser forces on molecule, a more recent subject despite the pioneer experiments [1,2], typically involve N ′′ = 1 → N ′ = 0 transitions (N is the rotational quantum number) between X 2 Σ(v ′′ = 0) and A 2 Π 1/2 (v ′ = 0) vibronic levels [3][4][5]. Including the electron spin leads to J ′′ = 1/2, 3/2 → J ′ = 1/2 transitions. Theoretical study of the correct choice of circular polarization for magnetooptical trapping depending on the angular momenta, J ′′ and J ′ , and on the g-factors, g ′′ and g ′ (respectively of the lower and upper states) has been performed in Ref [6]. It has been found heuristically that the trapping force is weak whenever g ′ is small compared to g ′′ . This is a serious limitation because in pure Hund's case (a) or (b), A 2 Π 1/2 does not present any Zeeman effect [7], so g ′ = 0 prevents any force. However experiments, such as that on SrF [8], were possible because of rotational and spin-orbit Π − Σ mixing allowing a small non zero value for g ′ (∼ 0.1 [6]). In addition to this weak force, J ′′ = 1/2, 3/2 → J ′ = 1/2 transitions present one or two dark states [9, 10] which leads to experimental difficulties if a stronger confining force is desired. Yet stronger force can be produced by rapidly switching the magnetic field gradient and laser beam polarization on a timescale (typically in the sub-microsecond range which is not a simple experimental task) preventing the adiabatic following of the atomic states as done in reference [3] .In this letter we suggest that efficient magneto-optical forces can be restored in all J ′′ → J ′ cases, even for g ′ = 0, in a very simple way, by simply adding one laser field of opposite polarization with a different detuning. We treat the simplest J → J − 1 case (that * Corresponding author: anne.cournol@u-psud.fr is J ′′ = 1 → J ′ = 0) and J → J case (that is J ′′ = 1/2 → J ′ = 1/2). An analytical one dimensional (1D) model is presented and help get t...