  Pebble transducers are nested two-way transducers which can drop marks (named
"pebbles") on their input word. Such machines can compute functions whose
output size is polynomial in the size of their input. They can be seen as
simple recursive programs whose recursion height is bounded. A natural problem
is, given a pebble transducer, to compute an equivalent pebble transducer with
minimal recursion height. This problem is open since the introduction of the
model.
  In this paper, we study two restrictions of pebble transducers, that cannot
see the marks ("blind pebble transducers" introduced by Nguy\^en et al.), or
that can only see the last mark dropped ("last pebble transducers" introduced
by Engelfriet et al.). For both models, we provide an effective algorithm for
minimizing the recursion height. The key property used in both cases is that a
function whose output size is linear (resp. quadratic, cubic, etc.) can always
be computed by a machine whose recursion height is 1 (resp. 2, 3, etc.). We
finally show that this key property fails as soon as we consider machines that
can see more than one mark.
