Vd and Cl effect on half-life

Effect of clearance and volume of distribution on half-life

The question arises how the volume of distribution (Vd), clearance (CL) and half-life are related. This figure illustrates two processes with a similar clearance mechanism (capable of clearing the same amount of volume of distribution per time). It is clear that it takes longer to remove all drug from the larger container.
However, what if the volume of distribution of both processes is similar, but the clearance mechanism of the lower container is much more efficient (i.e.

clears more drug)? The lower container will be cleared much faster. Half-life is therefore dependent upon both clearance and volume of distribution.
t½ = 0.693 × (Vd/Cl) or t½ = 0.693/k as seen with the elimination rate constant.
Furthermore, this allows us to calculate the clearance when the following equation is used Cl = k x Vd