Time delay interferometry (TDI) is a post-processing technique used in the Laser Interferometer Space Antenna (LISA) to reduce laser frequency noise by building an equal-arm interferometer via combining time-shifted raw phase measurements. The set of so-called 2nd generation TDI variables which sufficiently suppress laser frequency noise considering realistic LISA orbital dynamics has recently been expanded by a large number of additional solutions. In this paper, we characterize these new TDI channels by relating them to the well-known 1st generation variables $α$, $β$, $γ$, and $ζ$. We compute explicitly how each 2nd generation variable can be approximated as a linear combination of these four 1st generation variables, and show numerically that these approximations are accurate enough to model the noises not suppressed by TDI. We use these results to discuss how the newly found channels might be advantageous to use for the LISA data analysis. In addition, we demonstrate that newly found variants of the variable $ζ$ significantly out-perform the ones previously known from the literature.