We have investigated experimentally the magnetoresistance of strongly asymmetric double-wells. The structures were prepared by inserting a thin Al$_{0.3}$Ga$_{0.7}$As barrier into the GaAs buffer layer of a standard modulation-doped GaAs/Al$_{0.3}$Ga$_{0.7}$As heterostructure. The resulting double-well system consists of a nearly rectangular well and of a triangular well coupled by tunneling through the thin barrier. With a proper choice of the barrier parameters one can control the occupancy of the two wells and of the two lowest (bonding and antibonding) subbands. The electron properties can be further influenced by applying front- or back-gate voltage.