  Gardner conjectured that if two bounded measurable sets $A,B \subset
\mathbb{R}^n$ are equidecomposable by a set of isometries $\Gamma$ generating
an amenable group then $A$ and $B$ admit a measurable equidecomposition by all
isometries. Cie\'sla and Sabok asked if there is a measurable equidecomposition
using isometries only in the group generated by $\Gamma$. We answer this
question negatively.
