Honeycombs are widely used to laminarize fluid streams by inhibiting the lateral components of the fluctuating velocity. However, they also produce additional turbulence by themselves due to the formation of large-scale instabilities and the break-up of the individual velocity profiles stemming from the honeycomb cells. In the present research, we use 2D-planar particle image velocimetry (PIV) to study how honeycomb-generated turbulence is affected by a downstream grid. It is found that placing a grid near the honeycomb discharge drastically enhances flow uniformity by separating the strong jets stemming from the individual honeycomb cells into many smaller jets that are much more rapidly dissipated. Furthermore, the grid can reduce the magnitude of peak turbulence intensity by as much as 95%, as long as it is positioned upstream of the onset of the large-scale honeycomb-induced instabilities. A downstream grid is highly beneficial for both a laminar and turbulent honeycomb discharge and is most effective when there is a slight offset between the grid and honeycomb. Even though longer honeycombs generally produce more turbulence than short ones due to the larger length-scale of the shear layers, these effects are almost entirely decoupled when using a honeycomb-grid combination. Finally, a honeycomb-grid combination effectively inhibits both axial and lateral turbulence.