A novel design is described for an aperture that blocks a half-plane of the electron diffraction pattern out to a desired scattering angle, and then – except for a narrow support beam – transmits all of the scattered electrons beyond that angle. Our proposed tulip-shaped design is thus a hybrid between the single-sideband (ssb) aperture, which blocks a full half-plane of the diffraction pattern, and the conventional (i.e. fully open) double-sideband (dsb) aperture. The benefits of this hybrid design include the fact that such an aperture allows one to obtain high-contrast images of weak-phase objects with the objective lens set to Scherzer defocus. We further demonstrate that such apertures can be fabricated from thin-foil materials by milling with a focused ion beam (FIB), and that such apertures are fully compatible with the requirements of imaging out to a resolution of at least 0.34 nm. As is known from earlier work with single-sideband apertures, however, the edge of such an aperture can introduce unwanted, electrostatic phase shifts due to charging. The principal requirement for using such an aperture in a routine data-collection mode is thus to discover appropriate materials, protocols for fabrication and processing, and conditions of use such that the hybrid aperture remains free of charging over long periods of time.