  Fuzzy dark matter (FDM) with mass around $10^{-22}$ eV is viewed as a
promising paradigm in understanding the structure formation of the local
universe at small scales. Recent observations, however, begin to challenge FDM
in return. We focus on the arguments between the solution to CDM small-scale
curiosities and recent observations on matter power spectrum, and find its
implication on an earlier formation of small-scale structure. In this article,
we propose a scheme of k-ULDM scalar field with a differently-evolving sound
speed, thanks to the non-canonical kinetics. With the help of the
Dirac-Born-Infeld (DBI) theory, we illustrate to change the behavior of the
quantum pressure term countering collapse, therefore change the history of
structure growth. We find that it can truly reopen the ULDM mass window closed
by the Lyman-$\alpha$ problem. We will discuss such examples in this paper,
while more possibilities remain to be explored.
