Contents 
We show that for every positive integer $k$ there exists an interval map $f:I\to I$ such that:
(1) $f$ is LiYorke chaotic,
(2) the inverse limit space $\lim_{\leftarrow}\{f,I\}$ does not contain an indecomposable subcontinuum,
(3) $f$ is $C^k$smooth, and
(4) $f$ is not $C^{k+1}$smooth.
We also show that there exists a $C^\infty$smooth $f$ that satisfies (1)(2). This answers a recent question of P. Oprocha and J. P. Boronski from [\emph{On indecomposability in chaotic attractors}, preprint 2013], where the result was proved for $k=0$. 
