  We consider non-commutative deformations of sheaves on algebraic varieties.
We develop some tools to determine parameter algebras of versal non-commutative
deformations for partial simple collections and the structure sheaves of smooth
rational curves. We apply them to universal flopping contractions of length 2
and higher. We confirm Donovan-Wemyss conjecture in the case of deformations of
Laufer's flops.
