Scanning tunneling spectroscopy (STS) is a unique technique to probe the local density of states (LDOS) atthe atomic scale by measuring the tunneling conductance between a sharp tip and a sample surface. However,the technique suffers of well-known limitations, the so-called set-point effect, which can potentially introduceartifacts in the measurements. We compare several STS imaging schemes applied to the LDOS modulations ofthe charge density wave state on atomically flat surfaces, and we demonstrate that only constant-height STS iscapable of mapping the intrinsic LDOS. In the constant-current STS, commonly used and easier to implement,the tip-sample distance variations imposed by the feedback loop result in set-point-dependent STS images andpossibly mislead the identification of the CDW gap edge.