  We present a wide class of potentials which admit kinks and corresponding
mirror kinks with either a power law or an exponential tail at the two extreme
ends and a power-tower form of tails at the two neighbouring ends, i.e. of the
forms $ette$ or $pttp$ where $e, p$ and $t$ denote exponential, power law and
power-tower tail, respectively. We analyze kink stability equation in all these
cases and show that there is no gap between the zero mode and the beginning of
the continuum. Finally, we provide a recipe for obtaining logarithmic
potentials with power-tower kink tails and estimate kink-kink interaction
strength.
