Apparatus and methods for selectively and safely reversing flow in coiled tubing used for wellbore cleanouts are disclosed. One apparatus includes a section of coiled tubing having a main flow channel, at least two flow-preventing valves in the section of coiled tubing, each adapted to close the main flow channel upon attempted flow reversal; and at least one actuator adapted to deter closing of the flow-preventing valves. This abstract allows a searcher or other reader to quickly ascertain the subject matter of the disclosure. It will not be used to interpret or limit the scope or meaning of the claims. 37 CFR 1.72(b).