  Properly modulated flatband lattices have a divergent density of states at
the flatband energy. Quasiperiodic modulations are known to host a metal
insulator transition already in one space dimension. Their embedding into
flatband geometries consequently allows for a precise engineering and fine
tuning of mobility edges. We obtain analytic expressions for singular mobility
edges for two flatband lattice examples. In particular, we engineer cases with
arbitrarily small energy separations of mobility edge, zeroes, and
divergencies.
