  With the purpose of understanding how time delay interferometry (TDI)
combinations can best be used for the characterisation of LISA instrumental
noise, we revisit their laser frequency noise cancellation properties. We have
developed an algorithm to search for all possible combinations that suppress
noise at the same level as the X, Y and Z classical combination. The algorithm
calculates delays using symbolic formulas that explicitly include velocities
and accelerations of satellites up to the relevant order. In addition, once a
combination has been identified, delays are verified by solving numerically the
relevant equations using Keplerian orbits and Shapiro delay corrections. We
find that the number of combinations that suppress the noise is larger than
what was reported in the literature. In particular we find that some
combinations that were thought to only partly suppress the noise, in reality do
suppress it at the same level of accuracy as the basic X, Y and Z combinations.
