The possibility to induce real out-of-body experiences (OBEs) using hypnotic inductions, with the opportunity to interview participants during their experience, permits to investigate in depth the characteristics of different aspects of this particular state of consciousness from a first-person point of view. In this article, six selected participants report the description of another "body" we named "subtle body," identified as an intermediate entity between the physical body (Pb) and their "Self" or "I-identity" that was named "psychic body," and their relationships and characteristics. The "subtle body" was described as a sort of white silvered cloud surrounding the Pb, with a particular enlargement of its hands and feet that could move quickly like flying from one place to another even if less easily than the "psychic body," and a vague sense of attrition was perceived when passing through walls. Similar to the "psychic body," the "subtle" one too could move forward and backward in time even if they did not seem perceiving the sense of time. The "subtle body" was referred to be connected with the physical one by a sort of white brilliant link sometimes described like a silvered string more or less visible, whereas no visible links were identified between the "subtle body" and the "psychic" one. These reports were compared with similar descriptions deriving from the Vedanta philosophy and Theosophical tradition.