This work is motivated and exemplified by a genetic disorder causing early onset diabetes, blindness and deafness, which is extremely rare, inevitably fatal and has no current direct treatment. While the standard placebo-controlled RCT is the gold standard required by the regulatory agency for a new proposed drug study, it is conjectured that potential study participants will prefer a design which guarantees that they are always assigned to the drug under study. A single-arm design is proposed which meets this patient need and hence probably increases recruitment and compliance. At the same time, it meets the requirement for full randomization. Analyses which follow naturally from this design are also described and were used in trial simulations for sample sizing and for examination of the effect of underlying assumptions.