  Using a reverse-engineering approach on the time-distorted solution in a
reference potential, we work out the external driving potential to be applied
to a Brownian system in order to slow or accelerate the dynamics, or even to
invert the arrow of time. By welding a direct and time-reversed evolution
towards a well chosen common intermediate state, we derive analytically a
smooth protocol to connect two \emph{arbitrary} states in an arbitrarily short
amount of time. Not only does the reverse-engineering approach proposed in this
Letter contain the current -- rather limited -- catalogue of explicit protocols
but it also provides a systematic strategy to build the connection between
arbitrary states with a physically admissible driving. Optimization and further
generalizations are also discussed.
