The feasibility of implementation of asymmetric barriers (ABs) made of common materials for completely aluminum-free diode lasers is studied. The ABs adjoining a low-dimensional active region on both sides aim to prevent bipolar population in the waveguide layers and thus to suppress parasitic recombination therein, which in turn would enhance the efficiency and temperature-stability of the device. Our search algorithm for appropriate AB materials relies on the minimization of undesired carrier flow (electrons or holes passing through the active region toward the p- or n-type doped cladding layer, respectively), while maintaining the useful flows of hole and electron injection into the active region. Using an example of an 808-nm GaInAsP laser, it is shown that the n- and p-side ABs can be made, for instance, of GaInPSb and GaInP, respectively. In such a laser, the parasitic recombination flux can be suppressed by a factor of 60 for electrons and 200 for holes. It is found that the contribution of the indirect valleys to the electron flow through the p-side AB can be significant and even decisive in some cases. The contribution of light holes to the transmission through the ABs can also be considerable. The optimal thicknesses of the AB layers are determined and the chemical composition tolerances are estimated for a given flux suppression ratio. Published by AIP Publishing.