A realistic representation of convective boundary layers in large-scale models is a major goal of climate and NWP research. A major obstacle to the development of a unified parameterization of cloudy and clear convective boundary layers is the determination of the mixing length. In this work a new mixing length formulation for the eddy-diffusivity parameterization of PBL convection is suggested. This new formulation directly relates the mixing length with the square root of the turbulent kinetic energy through the use of a time-scale, and produces a realistic PBL growth and entrainment for dry convection. Sensitivity studies show that similarly positive results are obtained with a constant time-scale or with a time-scale proportional to h/w*. It is also shown that the model is extremely robust in terms of its sensitivity to different values of the surface flux and of the vertical resolution. The new formulation with an additional partition of the TKE into cloudy and clear values, produces realistic stratocumulus-topped (ASTEX) and cumulus-topped (BOMEX) boundary layers. Additionally, the new formulation has been able to produce realistic results for a case of shallow convection over land.