  We present a study of the Fermi surface of KFe$_2$As$_2$ single crystals.
Quantum oscillations were observed in magnetostriction measured down to 50 mK
and in magnetic fields $H$ up to 14 T. For $H \parallel c$, the calculated
effective masses are in agreement with recent de Haas-van Alphen and ARPES
experiments, showing enhanced values with respect to the ones obtained from
previous band calculations. For $H \parallel a$, we observed a small orbit at a
cyclotron frequency of 64 T, characterized by an effective mass of $\sim 0.8
m_e$, supporting the presence of a three-dimensional pocket at the Z-point.
