  We show that the celebrated operad of pre-Lie algebras is very rigid: it has
no "non-obvious" degrees of freedom from either of the three points of view:
deformations of maps to and from the "three graces of operad theory", homotopy
automorphisms, and operadic twisting. Examining the latter, it is possible to
answer two questions of Markl from 2005, including a Lie-theoretic version of
the Deligne conjecture.
