Self-tapping screws are the recognized state-of-the-art in fastener technology for timber structures. Combining fasteners of different stiffness, such as self-tapping screws with different installation angles, can be advantageous to simultaneously achieve high connection stiffness and ductility. In this paper, experimental investigations on a total of 65 glued-laminated timber joints assembled with a variety of installation angles including several combinations of self-tapping screws acting axially in withdrawal with self-tapping screws acting laterally are presented. The connection performance was analyzed in terms of the load-carrying capacity, the deformation capacity, the stiffness, and the ductility. The findings demonstrated that joint assemblies with self-tapping screws loaded primarily laterally exhibit low stiffness but high ductility, whereas joint assemblies with self-tapping screws loaded primarily in withdrawal are very stiff but exhibit low ductility. Combining screws in different installation angles created glued-laminated timber connections that combine high stiffness with high ductility. Existing analytical expressions were deemed suitable to estimate load-carrying capacity through simple summation of the different screws’ individual resistances.