General anesthesia can be caused by various, chemically very different molecules, while several other molecules, many of which are structurally rather similar to them, do not exhibit anesthetic effects at all. To understand the origin of this difference and shed some light on the molecular mechanism of general anesthesia, we report here molecular dynamics simulations of the neat dipalmitoylphosphatidylcholine (DPPC) membrane as well as DPPC membranes containing the anesthetics diethyl ether and chloroform and the structurally similar non-anesthetics n-pentane and carbon tetrachloride, respectively. To also account for the pressure reversal of anesthesia, these simulations are performed both at 1 bar and at 600 bar. Our results indicate that all solutes considered prefer to stay both in the middle of the membrane and close to the boundary of the hydrocarbon domain, at the vicinity of the crowded region of the polar headgroups. However, this latter preference is considerably stronger for the (weakly polar) anesthetics than for the (apolar) non-anesthetics. Anesthetics staying in this outer preferred position increase the lateral separation between the lipid molecules, giving rise to a decrease of the lateral density. The lower lateral density leads to an increased mobility of the DPPC molecules, a decreased order of their tails, an increase of the free volume around this outer preferred position, and a decrease of the lateral pressure at the hydrocarbon side of the apolar/polar interface, a change that might well be in a causal relation with the occurrence of the anesthetic effect. All these changes are clearly reverted by the increase of pressure. Furthermore, non-anesthetics occur in this outer preferred position in a considerably smaller concentration and hence either induce such changes in a much weaker form or do not induce them at all.