There are two conflicting interpretations of Einstein's light-speed constancy postulate, which he enunciated in his landmark 1905 paper on relativistic mechanics. The one that he proposed in his work was that the speed of light (c) in free space has the same value for all observers independent of their own state of motion (two years later he amended this position by stating that it only applied to cases where both the light pulse and the observer are at the same gravitational potential). A review of the relevant experimental data indicates, however, that there is a fundamentally more restrictive version of the light-speed constancy assumption which fits in better with the facts, namely that only the speed of light in free space relative to its source always has the same constant value, whereas the value relative to any given observer depends critically on the latter's state of motion. Particularly surprising is that Einstein's postulate leaves open the distinct possibility that the speed of light relative to its source can be as high as 2c, It is also interesting to note that, although Einstein's second postulate stands in direct contradiction to the predictions of the classical (Galilean) velocity transformation, there is no such conflict when the version which requires that the speed of flight in free space is only equal to c relative to the source from which it is emitted is used instead. Most telling is that it is found that the primary example Einstein used to illustrate his second postulate is actually inconsistent with the relativistic velocity transformation which he also derived in his original work on the basis of the same assumption.