Spectrally-selective photodetection via organic semiconductors manifesting narrowband absorption (NBA photodetection) is highly attractive for emerging applications that require ultrathin, lightweight, and low-cost solutions. While successful over mainstream color bands, NBA photodetectors have struggled so far to meet the functional and/or performance demands at longer wavelengths, importantly in the far-red (700-750 nm), a range relevant to diverse applications in analytical biology, medical diagnostics, remote sensing, etc. In consideration of the potential of a nonfullerene-acceptor route to address this challenge, the narrowband photodetection capabilities of SBDTIC, a recently-developed benzodithiophene-based acceptor with narrowband absorption in the far-red, are explored. Two bulk-heterojunction NBA configurations are considered, in which SBDTIC is combined with a donor either absorbing also in the far-red, or transparent through the visible. It is found that the latter configuration provides superior narrowband functionality, with peak detectivity of 1.42 x 10(13) Jones and spectral width of 141 nm-the highest detectivity to date for NBA far-red-selective photodetectors, and the smallest spectral width of all solution-processed implementations. In self-powered operation, such photodetectors additionally present a quasilinear response over a photocurrent range of least four orders of magnitude, and respond in the microsecond range, further evidencing the suitability of this approach to address the wealth of target applications.