  Time-Delay Interferometry (TDI) is the data processing technique that cancels
the large laser phase fluctuations affecting the heterodyne Doppler
measurements made by unequal-arm space-based gravitational wave
interferometers. The space of all TDI combinations was first derived under the
simplifying assumption of a stationary array, for which the three time-delay
operators commute. In this model, any element of the TDI space can be written
as a linear combination of four TDI variables, the generators of the
"first-generation" TDI space. To adequately suppress the laser phase
fluctuations in a realistic array configuration, the rotation of the array and
the time-dependence of the six inter-spacecraft light-travel-times have to be
accounted for. In the case of the Laser Interferometer Space Antenna (LISA), a
joint ESA-NASA mission characterized by slowly time varying arm-lengths, it has
been possible to identify data combinations that, to first order in the
inter-spacecraft velocities, either exactly cancel or suppress the laser phase
fluctuations below the level identified by the noise sources intrinsic to the
heterodyne measurements (the so called "secondary" noises). Here we reanalyze
the problem of exactly canceling the residual laser noise terms linear in the
inter-spacecraft velocities. We find that the procedure for obtaining elements
of the $2^{\rm nd}$-generation TDI space can be generalized in an iterative
way. This allows us to "lift-up" the generators of the $1^{\rm st}$-generation
TDI space and construct elements of the higher order TDI space.
