Magnetic fields are present in roughly 10% of white dwarfs. These fields affect the structure and evolution of such stars, and may provide clues about their earlier evolution history. Particularly important for statistical studies is the collection of high-precision spectropolarimetric observations of (1) complete magnitude-limited samples and (2) complete volume-limited samples of white dwarfs. In the course of one of our surveys we have discovered previously unknown kG-level magnetic fields on two nearby white dwarfs, WD 1105-340 and WD 2150+591. Both stars are brighter than mV=15. WD 2150+591 is within the 20pc volume around the Sun, while WD 1105-340 is just beyond 25pc in distance. These discoveries increase the small sample of such weak-field white dwarfs from 21 to 23 stars. Our data appear consistent with roughly dipolar field topology, but it also appears that the surface field structure may be more complex on the older star than on the younger one, a result similar to one found earlier in our study of the weak-field stars WD 2034+372 and WD 2359-434. This encourages further efforts to uncover a clear link between magnetic morphology and stellar evolution.