Spin-transfer torque in a class of magnetic tunnel junctions with noncollinear magnetizations, referred to as spin filter tunnel junctions, is studied within the tight-binding model using the nonequilibrium Green's function technique within Keldysh formalism. These junctions consist of one ferromagnet (FM) adjacent to a magnetic insulator (MI) or two FM separated by a MI. We find that the presence of the magnetic insulator dramatically enhances the magnitude of the spin-torque components compared to conventional magnetic tunnel junctions. The fieldlike torque is driven by the spin-dependent reflection at the MI/FM interface, which results in a small reduction of its amplitude when an insulating spacer (S) is inserted to decouple MI and FM layers. Meanwhile, the dampinglike torque is dominated by the tunneling electrons that experience the lowest barrier height. We propose a device of the form FM/(S)/MI/(S)/FM that takes advantage of these characteristics and allows for tuning the spin-torque magnitudes over a wide range just by rotation of the magnetization of the insulating layer.