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.