This work continues our previous work [1] and in a more developed form [2]), on electron deep orbits of the hydrogen atom. An introduction shows the importance of the deep orbits of hydrogen (H or D) for research in the LENR domain, and gives some general considerations on the EDO (Electron Deep Orbits) and on other works about deep orbits. A first part recalls the known criticism against the EDO and how we face it. At this occasion we highlight the difference of resolution of these problems between the relativistic Schrödinger equation and the Dirac equation, which leads for this latter, to consider a modified Coulomb potential with finite value inside the nucleus. In the second part, we consider the specific work of Maly and Va’vra [3], [4]) on deep orbits as solutions of the Dirac equation, so-called Deep Dirac Levels (DDLs). As a result of some criticism about the matching conditions at the boundary, we verified their computation, but by using a more complete ansatz for the “inside” solution. We can confirm the approximate size of the mean radii of DDL orbits and that decreases when the Dirac angular quantum number k increases. This latter finding is a self-consistent result since (as distinct from the atomic-electron orbitals) the binding energy of the DDL electron increases (in absolute value) with k. We observe that the essential element for obtaining deep orbits solutions is special relativity.