  The search for continuous gravitational waves from unknown isolated sources
is computationally limited due to the enormous parameter space that needs to be
covered and the weakness of the expected signals. Therefore semi-coherent
search strategies have been developed and applied in distributed computing
environments such as Einstein@Home, in order to narrow down the parameter space
and identify interesting candidates. However, in order to optimally confirm or
dismiss a candidate as a possible gravitational-wave signal, a fully-coherent
follow-up using all the available data is required.
  We present a general method and implementation of a direct (2-stage)
transition to a fully-coherent follow-up on semi-coherent candidates. This
method is based on a grid-less Mesh Adaptive Direct Search (MADS) algorithm
using the F-statistic. We demonstrate the detection power and computing cost of
this follow-up procedure using extensive Monte-Carlo simulations on (simulated)
semi-coherent candidates from a directed as well as from an all-sky search
setup.
