  We present a next-to-leading order accurate simulation of t-channel
single-top plus jet production matched to parton showers via the POWHEG method.
The calculation underlying the simulation is enhanced with a process-specific
implementation of the multi-scale improved NLO (MINLO) method, such that it
gives physical predictions all through phase space, including regions where the
jet additional to the t-channel single-top process is unresolved. We further
describe a tuning procedure for the MINLO Sudakov form factor, fitting the
coefficient of the first subleading term in its exponent using an artificial
neural-network. The latter tuning, implemented as a straightforward
event-by-event reweighting, renders the MINLO simulation NLO accurate for
t-channel single-top observables, in addition to those of the analogous
single-top plus jet process.
