Scenarios of new physics where a single top quark can be produced in association with large missing energy (monotop) have been recently studied both from the theoretical point of view and by experimental collaborations. We revisit the originally proposed monotop setup by embedding the effective couplings of the top quark in an SU(2)L invariant formalism. We show that minimality selects one model for each of the possible production mechanisms: a scalar field coupling to a right-handed top quark and an invisible fermion when the monotop system is resonantly produced, and a vector field mediating the interactions of a dark sector to right-handed quarks for the non-resonant production mode. We study in detail constraints on the second class of scenarios, originating from contributions to standard single top processes when the mediator is lighter than the top quark and from the dark matter relic abundance when the mediator is heavier than the top quark.