  We discuss a new class of tribrid inflation models in supergravity, where the
shape of the inflaton potential is dominated by effects from the K\"ahler
potential. Tribrid inflation is a variant of hybrid inflation which is
particularly suited for connecting inflation with particle physics, since the
inflaton can be a D-flat combination of charged fields from the matter sector.
In models of tribrid inflation studied so far, the inflaton potential was
dominated by either loop corrections or by mixing effects with the waterfall
field (as in "pseudosmooth" tribrid inflation). Here we investigate the third
possibility, namely that tribrid inflation is dominantly driven by effects from
higher-dimensional operators of the K\"ahler potential. We specify for which
superpotential parameters the new regime is realized and show how it can be
experimentally distinguished from the other two (loop-driven and
"pseudosmooth") regimes.
