  We report on simulations of mildly turbulent convection in spherical wedge
geometry with varying density stratification. We vary the density contrast
within the convection zone by a factor of 20 and study the influence of
rotation on the solutions. We demonstrate that the size of convective cells
decreases and the anisotropy of turbulence increases as the stratification is
increased. Differential rotation is found to change from anti-solar (slow
equator) to solar-like (fast equator) at roughly the same Coriolis number for
all stratifications. The largest stratification runs, however, are sensitive to
changes of the Reynolds number. Evidence for a near-surface shear layer is
found in runs with strong stratification and large Reynolds numbers.
