We have performed Hartree-Fock calculations of the electronic structure of N ≤ 10 electrons in a quantum dot modeled with a confining Gaussian potential well. We discuss the conditions for the stability of N bound electrons in the system. We show that the most relevant parameter determining the number of bound electrons is V
2. Such a feature arises from widely valid scaling properties of the confining potential. Gaussian Quantum dots having N = 2, 5, and 8 electrons are particularly stable in agreement with the Hund rule. The shell structure becomes less and less noticeable as the well radius increases.