Developed as an extension of the earlier D3 correction, the D4 dispersion model introduces several innovations, including a more sophisticated treatment of atomic polarizabilities, redefined expression for atomic coordination numbers, and accounting for the partial atomic charges in the molecular environment. It is therefore natural to ask whether the D4 model is also prone to induce potential energy surface distortions similar to those demonstrated recently for D3. Addressing this question is the first purpose of this letter, and we shall show that while D4 is much less prone to these artifacts than D3, their fundamental cause is not eliminated entirely. The D4 model's greater complexity makes it difficult to understand if the fixes similar to those introduced to amend D3 would work here. Therefore a second purpose of this letter is to explore suitable modifications to the D4 dispersion model with the goal of removing the appearance of artifact geometries and unphysical kinks in potential energy surfaces without compromising its thermochemical performance.